IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


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12.2 

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Photographic 

Sciences 

Corpomtion 


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23  WESf  MAIN  STREET 

WEBSTER,  N.Y.  14S80 

(716)  372-4503 


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CIHM/ICMH 

Microfiche 

Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  canadien  de  microreproductions  historiques 


:<^ 


Technical  and  Bibliographic  Noius/Notes  techniques  et  bibliographigues 


The  Institute  has  attempted  to  obtain  the  best 
original  copy  available  for  filming   Features  of  this 
copy  which  may  be  biblingraphically  unique, 
which  may  alter  any  of  the  images  in  the 
reproduction,  or  whici,  may  significantly  change 
the  usual  method  of  filming,  are  checked  below. 


L'Institut  a  microfilme  le  meilleur  exemplaire 
qu'il  lui  a  ete  possible  de  se  procurer    Les  details 
de  cet  exemplaire  qui  sont  peut  etre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifiHr 
une  image  reproduite,  ou  qui  peuvent  exigsr  un.} 
modification  dans  la  m^thode  normaie  de  filmage 
sont  indiqu^s  ci  dessous 


□ 


Coloured  covers/ 
Couverture  de  couleur 


□ 


Coloured  pages/ 
Pages  de  couleur 


□    Covers  damaged/ 
Couverture  endommag^e 


n 


Pages  damaged/ 
Pages  endommagees 


□ 


Covers  restored  and/or  laminated/ 
Couverture  restaur6e  et/ou  pellicul6e 


c 


Pages  restored  and/or  laminated/ 
Pages  restaur^es  et/ou  pelliculees 


V 


Cover  title  missing/ 

Le  titre  de  couverture  manque 


I       I    Pages  discoloured,  stained  or  foxed/ 
I I    Pages  decolorees,  tache;ees  ou  piquees 


G 


Coloured  maps/ 

Cartes  g^ographiques  en  couleur 


□ 


Pages  detached/ 
Pages  detachees 


n 


Coloured  ink  (i.e   other  than  blue  or  black)/ 
Encre  de  couleur  (i  e   autre  que  bleue  ou  noire) 


I       I    Showthrough/ 
Transparence 


D 


Coloured  plates  and/or  illustrations/ 
Planches  et/ou  illustrations  en  couleur 


n 


Quality  of  print  varies/ 
Qualite  inegale  de  I'impression 


Bound  with  other  material/ 
Relie  avec  d'autres  documents 


D 


Includes  supplementary  material/ 
Comprend  du  materiel  supplementaire 


D 


Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

Lareliure  serree  peut  causer  de  I'ombre  ou  de  la 
distortion  le  long  de  la  marge  int6rieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text    Whenever  possible,  these 
have  been  omitted  from  filming/ 
II  se  peut  que  certaines  pages  blanches  ajout^es 
lors  dune  restauration  apparaissent  dans  le  texte, 
mais,  lorsque  cela  6tait  possible,  ces  pages  n'ont 
pas  ete  film6es. 


n 


Only  edition  available/ 
Seule  Edition  disponible 

Pages  wholly  or  partially  obscured  by  errata 
slips,  tissues,  etc.,  have  been  refilmed  to 
ensure  the  best  possible  image/ 
Les  pages  totalement  ou  partiellement 
obscurcies  par  un  feuillet  d  errata,  une  pelure, 
etc.,  ont  ete  filmees  ci  nouveau  de  facon  a 
obtenir  la  meilieure  image  possible 


D 


Additional  comments:/ 
Commentaires  supplementaires: 


This  item  is  filmed  at  the  reduction  ratio  checked  below/ 

Ce  document  est  film6  au  taux  de  reduction  indiqu^  ci-dessous. 

22X 


10X 


14X 


18X 


26X 


30X 


/ 


12X 


16X 


20X 


24X 


28X 


32X 


The  copy  filmed  h'»ro  has  been  reproduced  thanks 
to  the  generosity     f 

L'oriiry  of  Corxiross 
PhotuduplicatJon  Service 


L'»XL'mf)lc«ir»!  filfn«^  tut  roproduit  qr«i<;e  .1  la 
96n^r(jsit(^  de 

Library  of  CorujrHss 
Pfiotodupliciitiun  Servicw 


The  images  appe«3ring  hero  are  the  best  quality 
possible  considering  the  condition  and  legibility 
of  the  original  copy  and  in  keeping  with  the 
filming  contract  specifications. 


Les  images  suivantes  ont  dt^  reproduites  avec  le 
plus  grand  soin,  compte  tenu  de  l<i  condition  et 
de  la  nettHt6  de  I'exemplaire  film6    ot  on 
conformity  dvec  les  conditions  du  contrat  de 
filmage. 


Original  copies  in  printed  paper  covers  are  filmed 
beginning  with  the  front  cover  and  ending  on 
the  last  page  with  a  printed  or  illustrat'id  impres 
sion,  or  the  back  cover  when  appropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
first  page  with  a  printed  or  illustrated  impres 
sion,  and  ending  on  the  last  page  with  a  printed 
or  illustrated  impression. 


Les  exemplaires  originaux  dont  la  couverture  en 
papier  est  imprim^e  sont  film^s  en  commencant 
par  le  premier  plat  et  en  tarminant  soit  par  la 
derni^re  page  qui  comporte  une  empreinte 
d  impression  ou  d  illustration,  soit  par  le  second 
plat,  selon  le  cas   Tous  les  autres  exemplaires 
originaux  sont  film6s  en  commencant  par  la 
premiere  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  pai 
la  derni^re  page  qui  comporte  une  telle 
empreinte 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  — ^  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning     END"), 
whichever  applies. 


Un  des  symboles  suivants  apparaitra  sur  la 
derni6re  imago  de  chaque  microfiche,  selon  le 
cas:  le  symbole  — ♦•  signifie     A  SUIVRE",  le 
symbols  V  signifie     FIN". 


fy/laps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios   Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method; 


Les  cartes,  planches,  tableaux,  etc  ,  peuvent  etre 
film6s  ci  des  taux  de  reduction  diff6rents 
Lorsque  le  document  est  trop  grand  pour  etre 
repioduit  en  un  seul  cliche,  il  e.st  film^  A  partir 
de  Tangle  sup6rieur  gauche    de  gauche  d  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d  images  necessaire.  Les  diagrammes  suivants 
illustrent  la  m^thode. 


t 

2 

3 

32X 


1 

2 

3 

* 

5 

6 

na 


am 


TEACHERS'    MANUAL 


KOK 


FREEHAND   DRAWING 


IM    PRIMARY    SCHOOLS, 


II  V 

Prok.  WALTEP.   smith, 

STATB   DIRKCTDR  of   AKT    KDUCATIO.I   roR   MASfACIIUSRTTS. 


InltndKl  to  iccomfMny  the  American  Drawing-Ctrdi,  by  th*  lime  authoi. 


/?iiiLi 


,N' 


BOSTON:   < 
JAMES   R.  OSGOOD   AND  COMPANY, 

(l.ATR  TtCKNOR  A  FIELDS,  AND  riBI.DS,  OSGOOD,  A  CO.) 
1874. 


V  » 


H 


Entered  nccording  to  Act  nf  Congreu,  in  tlic  ycir  1873,  by 

JAMKS    K.   OSGOOD  &  CO., 
In  the  Office  of  the  Librarian  of  Congreu  at  Washinginn. 


(tf 


Boston  ! 

R.-.ND,    AVHKV,    &    *'<>.,    KURCTKOTVPKKS    AND    PrIMTIIIIS. 


I 

r 


o 


(0 


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e,\r  iH;3,  by 
Waihinnlon. 


n  Primtkhs. 


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i    - 


V 


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COIS  TENTS. 


Fa«»., 
iNTKOnJKJTION ^         .         .  a 

Ckntkk,  I'ointm,  and  Htkakiht  Lwrh     t       »       ,       .10 

HTIIAKIIIT  lil.NK   KldlTHEH 40 

HiMi'i.K  ci'HVKH nn 

CUMI-UU.ND  CUUVBH.  — EM.II'SK  AND  OvAI.  .72 

Compound    <!i;uvk».  — Ukvih^kd   C'uiivks,   tiik;   Ookk 

AND  AbsTUAI.T  CUHVKN )M( 

I'ltACTicAi,  Dehkin inn 

I'UAfTrcAI.       DksKIN.  —  LkAVKW,      IUU«,      and      FiXiWKKH 

CONVKNTIONAI.tZED lit;! 

I'liAcTHAi.    Dkhkin. —Fruit,  Compound  Lkavkm,  and 

Sl'UIOS   CONVKNTIONALIZKD      .  .  .  .       •  .  .       IWt 

FoiiMH  or  Leavkh  and  Flowers       .  .       ►  I.'>!i 


.  I 


.  \ 


INTRODUCTION. 


That  it  in  pructicuhlo  to  teach  tlrawiiiK  i»  <••«' 
piililir  Hfliooln  iii  no  loiigor  a  niiUtcr  of  doubt ;  uiid 
tliiit  til.'  Mtiiily  in  oiii'  of  ^,'rciit  imluMtriftl  iiiul  filiicii- 
tioiitil  viiliif,  wlicii  jiropi'rly  tiiiinlit,  no  pfr-xn,  who 
luirt  nircfully  invcctiKiitcil  ilic  miliji-ct,  qucMtioMn  for  ii 
monu>nt.  Tin'  tlrtivvinn,  liowovur,  inuMt  Im  wiilo  in  itn 
riinnf,  nitiohiil,  iiinl  Hyrtti'iniitic.  It  numt  !•••  niuili 
niort'  timn  Niniplit  (:r)pyiny :  indi'cd,  it  niuxt  In-,  in  tin 
miiin,  Homctliing  wholly  dittertnt  froni  tlnit  ;  iind  it 
must  ho  much  nioru  thiui  pirturt^-nnikin),', — I'vi-u 
>;o()d  orininiil  pictun'-nuikiiiK-  Thorn'  who  think 
oihcrwirtc  Hiully  inisnpi)r('ht'nd  tho  woj)*^  and  vahn;  of 
one  of  tin*  nnwt  practiital  studii'«. 

It  will  ho  olwiTVi'd,  as  chariutoristii;  of  this  course 
of  drawiu);,  both  in  its  prinniry  and  udvaiu-cd  ^radex, 
that  the  pioture-tdoment,  an  »uch,  in  iilmost  entirrly 
excluded.  The  iiuthor  is  well  aware,  that,  in  j'xclud- 
iuR  many  pretty  thiuf^s  which  have  usually  been  con- 
sidered proper  for  drawiuR  exercises,  he  sacrilices 
something  of  superlicial  attractiveness;  Init  he  omits 
them  because  tlie  best  artistic,  practical,  or  educa- 
tional results  cannot  otherwise  be  produced.  lie 
excludes  them  from  even  this  primary  course,  because 
he  would  here  lay  a  sound  basis  for  more  advao'cd 
and   severer  work,  when   pupils   reach    the   granunar 


TK.WUKI/y    U.iyi'AL 


m'\umU.  Mt'iiri',  wliili-  tlif  lUitlior  U  ftwnrf  lliut 
|Mi|iiU  iirt>  iiiixiiiiiN  to  lH>|{ih  wliut  tuny  Im>  i'iillt>i| 
"  jirxtty  work,"  iih  I'urly  iix  |ini«i«ili|i<,  )ii>  wImIu'm  ii>iirli- 
fi-M  I'Irarlv  III  iiiiili'i-Htuiiil  tliitt  iiictiiri'Miitikiiiu.  no  i'lir 
ilH  tlit>  piiltlii!  HflioolH  ur«*  coiii-i'rtiiul,  mImiiiM  iilwuyit  Imi 
ri"4aril)'i|  uh  ii  HcioiHliirv  tiiuttcr.  lit*  uImo  wixlion 
ti-iK-liiTH  til  ri'iiii'iiilM'r  tliiil  tin-  corri'i't  ri'pn'Ki'ntft- 
tinii  of  any  olijfrt,  itit  rt'iilly  hc(>ii,  itivolvctt  priti- 
liplcrt  of  |H'rMp*>ctiv<s  with  lii^lit  iimi  nIiimIi',  wlii<;)i 
yoiiM^  pupiN  nuinot  iiiMli>rNtaii<l ;  wliidi  cikiiiiot, 
iiiili'cil,  In-  umltTHtood  hy  uny  rnic  without  tiiiiih 
hiinl  tttiiily,  Httiicx,  to  mt  rhihiroti  ilruwitiK  frmii 
I'opii-M  involving  tlwxt*  It'ittmcH  in  to  mtt  tlioiii  to  r<>pro- 
tliii'iii^,  ill  II  incri'ly  inccliiiiiicul  wiiy,  whiit  they  cunnot 
posxilily  coniprt'ht'inl.  riiHtciiil  of  li'iuiiiiK  h'lirni'rii 
into  Hiich  riitH,  the  author  dtmireH,  lirNt  of  nil,  to  tiiitko 
thciii  ii('i|iiiiiiit«il  with  the  hfuiiticx  of  piirt'  form  iiiul 
with  tlic  principIi'M  of  k"">I  <I»'(*i>,'n.  Thcrffon-,  it 
is  tliiit  the  fxiTciNi'M  in  thiH  prinnuy  foiirHc  arc  priii- 
ci|ially  Miu-li  tw  tlcal  vvitli  incn-  oiitliiii>  ri*pri*N<-iitatiiin, 
buHttil  on  ({I'iiiiii'ti'ical  foriiiK,  ami  iniistratiiij^  h'lulin^ 
priiu'ipli'H  of  practical  dfHign.  It  is  only  wlieii  pupils 
have  well  iiiaHtt'rciI  thiN  Mtagc  that  they  arc  pn-pait-il 
to  tiikf  up  intclligiMitly,  ami  in  a  thorough  nmiincr, 
pcrspft'tivc,  anil  luoild  unil  ohjm't  drawing. 

IIK.VWINU    HHOIM.II     UK    TAIMJIIT     IIV     KKIICI.AU 
TKArllKltS. 

Drawing  i-aii,  ami  hIioiiIiI,  l>t>  taught  hy  thi>  rogular 
tt'aoher.  One  who  umliTstamls  the  gi-neral  prinriples 
of  ti'iiching  i!iin  toai'h  drawing  HUcct'HHfully,  without 
any  special  artistic  gifts.     Thousands  of  persons  teach 


i 


rnrt'    tlint 

IIK  t<>ltr||< 

i«.  HO  fur 

10  wixlioii 
'lin'Ht'litft- 
vi'H  prill- 
li<,  which 
I  cuiiiiot, 
Hit  iniicli 
iiiK  (mm 
I  to  rc|>ro> 
«>y  cumiot 
IcuriDTH 
,  to  iiiikkt 
r<iriii  iiiid 
rd'oii',  it 
uri>  priii- 
^(•iitiition, 
g  li'Uiliiif^ 
uii  |iii|iils 
|in'|iar('il 


lULAlt 

f  ri'nijliir 
|)i'ii>('i|il<-.s 
,  witliiiut 
oils  tcucl) 


ISTHiWUCItOtf.  f 

MrittlllU'tii'  MIllTDNIlfully  will)  \W*MM  no    ll|M'i'iul    llUtttll'- 

ntittiiMl  ((iflx;  tiiitl  tlit'rc  it)  iiotliiii^  a)K)Ut  ilruwiii^  mo 
tlirticuU  til  iiiiixtt-r  ui*  xoiiii'  III'  lilt'  I'ftitiiri'H  of  mutlM*- 
nmtiut,  L<*t  it|  tln'ii,  li«>  iti'c«i|itfil  um  true,  tliitt  there 
In  nothing  ithotit  ilniwin^  to  prevenl  uiiy  perKuii  of 
fitir  riipiu'ity  heroiniii^  |>ri>ll<'ii'iit  enough  to  teiuli  it 
iiitelli^etilly  mill  vvith  miiiri'HM.  It  in  cle'ir,  from  tin- 
preneiit  iiioviMiieiit  in  fitvor  of  art  eiliiciitioii,  that  the 
teuchiiiK  of  ilrit\viiii(  will  loon  he  reipiin  d  in  ull 
piililii*  hi'IiooIm;  and  it  iiiiiNt,  therefore,  lie  tiiiii^ht  liy 
the  ri'i^iiliir  teucherM.  Itnleeil,  it  in  bunt,  for  various 
roiMoiiM,  that  it  hIioiiM  thiiM  be  tuuijht, 

TlIK    OIUKCT    OK    TIIIH    fniMAHV    COl'liSB. 

Thiit  Manual,  with  thiM-anU  wliiuh  lux'onipiUiy  it,  irt 
ititemleil  fur  a  i-oui'mu  of  iiottriii'tion  in  nlate-ilrawing 
in  primary  Hchoolx.  The  uxercines  uru  «o  Miinplc,  ami 
Ml  ^ruilnk(!ly  pro^ruKMive,  that  tencliurM,  though  they 
may  have  liiul  no  pruviouH  iiiHtnuition  in  drawing,  can 
nnirtter  them,  if  they  cliooMe.  without  anniHtunce,  and 
intelligently  lead  any  class  of  young  ptipiU  who 
hnppiMi  to  Im  under  their  charge.  There  In  nc  better 
way  to  teach  oui-'m  self  than  leucliing  others.  With 
the  cards  in  the  hands  of  the  pupils,  furniithiiig  them 
good  copit'H,  it  is  not  at  all  essential  that  teachers 
should  bo  extraordinarily  ukilful  in  drawing  on  the 
blackboard.  The  Manual  will  acquaint  them  with 
all  the  principles  involved:  these  principles  they  can 
explain  orally  to  the  pupils.  It  is  the  clear  xetting 
forth  of  these  principles  that  constitutes  the  feature 
of  chief  importance  in  teaching  drawing.  The  ptqiils, 
with  their  card  copii's  before  them,  aided  by  the  oral 


TMAVllt^nfl*  M.tSUAL 


••x|>l!ii>!itii»),  iuhI  l>y  »)i)'h  lllii!>tritti*.>ii!>  (vyt*ii  tli'>ui;)i 
llii'v  Im'  rtiil<')  li*  (III-  ii'iu'lii'r  limy  |{ivc  on  thi'  iMNinl, 
Hill  ihuki'  vi'ry  <«nt:»fm  toi-y  \>t»ittvn». 

It  i>«  tliK  li'u<liM|j  iiliji't't  of  tli«>«i>  I'lirlit  to  trMh 
pi>i|Mirtiitii,  till-  '•iiii|)l<>  ll^iiri'M  of  |iluiii*  |{i»iiiM>(ry,  tli* 
iit'iiK  i|*li"*  "t  |>riMii<  itl  •Itiai^n,  lUiii  to  laiiiiliitri/i<  the  pu- 
pil uitli  iM-uiitiliil  toriiiii.  To  iiiiiiii'ilmti'ly  lollow  {\\v*v 
uurtlN  ill  tlui  uppi<r  eliiMMm  of  priinitry  mi'IkhiId,  or  in 
iiitttriiK-iliiklit  m<-1ioo|m,  tint  aullinr  Iium  pr^'purc  I   tlirt'i* 

Minull  IxHitot  ill  fr Iittn<l  iiruwiii((,  to  In-  iihi-iI  liy  piipiU 

ill  lic^iiiiiiiiK  to  ilruw  oil  piipir.  'riii>  cxcrciiii't  in  iIu'mk 
liiHikM  iipply  till-  priiii'ipli-M  of  tlio  itiMtriu'tioii  ^Ivi'ii  iti 
till'  t'iir<l-«yiirciMi'i«,  utiil  ti'ii(*li  inoi'i>  fully  iIm'  ilruwiiiK 
ill  oiitliiiu  uf  objticti  with  ri'^uiur  fuuturuit. 

IlKUirrTION   \SU   KNt.ABllKMBVT. 

Ti'iidicrM  mIioiiIiI  iiiiilto  tlii'iiiNi'lvcH  Hiitliiiciitly  lit- 
iiiiliiir  with  tlio  I'MTfiMCM,  liy  dniwiiiK  tliciii,  to  Ik- 
iilili*  to  point  out  tlifir  I'l'itturt'M  rt'iulily  iiml  tifitrly. 
Wlii'ii  woikiiif{  on  till'  hliK'klioiinl,  tlit-y  xlionld  pro- 
ci'i'il  nlowly,  i'Xplaiiiinv(  I'Uih  point  as  tlify  go  ulon((, 
uiui  rci|ttiriii|{  tint  wliolt*  i;Iiimn  to  work  tiiKi-tln'r,  I'Vcn 
tlioiigli  Monit'  urc  oliliK*'*!  t"  I'xccuti'  their  tirivwingii 
vciy  rnili'ly. 

It  in  iiiti'tiih'd  tliut  tlni  fif|uri>H  givnn  in  thi'  lirnt 
chiiptiir  of  tliii  MniDial  hIiuII  Ix*  ilrawn  on  thi'  hliu-k- 
lionnl  liy  the  ti'iuhci  to  u  niuIc  of  one  foot  for  i-vi'ry 

Iiiilf  inch  of  tin py.     Tln'ii  tlio  pnpiln  nn-  to  lopy 

tiii'in  on  their  »lati'H,  making  thi-in  of  a  ih>lliiiti<  h!  i' 
Mtwti'd  by  the  teacher.  Thu  Hi/u  of  the  flguri'H  w  ill  he 
goviTiind  hy  tho  »izt'  of  the  piipiln'  nliiti'M.  Tliix  will 
tt'ach  nduv.tiun.     It  w  intouded  that  i\w  lorniM  on 


•    T* 


4 


ISTHOIWVriUS,  -       w- 

tiiti  \iM\\*  »\\vA\  iw  t;«»t>ieil  hy  thu  |»ii|))it  l'^Ml)  tlit*  lanUt 
ltii>  ti'iM'tiiT  iiMlit  iitiiiK  tilt'  |iri)|Hirl*  MtM,  or  Mtttl*',  wliiili 
(•limilil  Ih<  iimk  Ii  larger  ilntit  iii  tin'  r)i|i).  TliU  hIU 
lino'li  ih»  |Mi|iilN  I  ii/iififi  III!  iif.  'I'tx'  iMii  Icitttir*'*  iif 
priu'tlfi*,  ri'ilin'tioii  iimt  i'iilit.'t{iMii<Mit  fn>tn  i'i>|iictf, 
nImmiIiI  ko  ttij(i'lln'r :  iHith  iii''  i'»M'iif  iul  »<•  K'»hI  |irt(. 
)(ri>B>«  ill  <imvviii((.  Ii  iiuli  |iii|iil  it  »M|i|ilii'<|  »itli 
I'linl  «'i»|tii'i«,  ilii)  liklMir  of  till'  fi-mliiT  wilt  Ih»  jrn ally 
iiliri<l((i<«l ;  HiiifK  nil  run  lii<  tiiiiulit  tin-  •iiiiiii>  tiling  iit 
tlii>  *uini'  tinii>,  \vliili>  tin-  lulvuiH'i'iiii'iif  of  tlu'  «lioli' 
rlium  kvill  li«>  liiiin*  xittiMt'iM'tory  tliiiii  it  tun  !)•<  i>tlii'i'wi-<i'. 
Till'  tl|{iiri'N  kIvi'ii  ill  till'  otliiT  i-liii|iti>rii  of  tlii'  Mini- 
mil,  uikI  not  rotiml  on  tlii<  i-unU,  ui'«  iiiti>iii|i>il  for 
lilui'kliounl  i-o|iii>M.  to  lie  tiruwii  liy  tin'  li-uilirr  iin 
iiitroiliictoiy  I'xiT.'iKi'K  to  till'  iiKi'  of  till'  I'upU,  or  lor 
tlirtntioii  i>xi>n-ii«*M  ta  iii'i>iiiii|iuiiy  tlii>  ruiiU. 


ilROMKTKlr.VI.    IlKKINITIllVM. 

Tlii«  ilfiliiitioiiH  of  |iluiii*  Ki'oiiiftry,  illiixtrutioiit  of 
wliii'li  Mv  I'liiplovfil  \\n  u  liuni^  of  fri'i'liuml  iliuwiiiK, 
mIioiiIiI  I'I'  nivtii  to,  uMil  ri'|H'iUt'<l  l>y,  tlio  yoimni'Ht 
liiipili.  Tlii-y  hIioiiIiI  I)i>  i>x|iluiiii'il,  not  mi  iiiih'Ii  liy 
\vor<U,  iiM  liy  friM>li>in<l  illiii»trutioiiM  iliuwii  on  tin- 
liluikliounl  UK  uiitiiuti'ly  uh  poKHil.lc.  l''iKiiri'H  of 
thin  kinil,  wImmi  hi-i'ii,  fliililini  n'lulily  iiiiiIitmIuihI. 
Tlio  cojiK'H  in  tli«  llrnt  oliiiptfr  iiiuy  Iw  ivpiuitcil  nn 
often  HH  writing  IcKHoim;  Init,  iiiHti-uil  of  (•oiitinuiil 
ifpctitioiiK  of  till-  Huiiii-  fxiTciHc,  tlu'  wliolc  Ki'iii's  in 
ili<<  lii'Ht  ohupti-r  nIioiiI(|  Im>  ^oiii*  ovi-r  oiiri>,  ami  tlifii 
111'  tukim  u^'^in  from  tlii«  llrHt,  with  u  ln-tti-r  umlfi- 
Ktumliii;?  uml  iiirri'uxfd  wkill.  Wlicii  tcuiliiii;,'  <liil- 
ilrtfii  to  druvv,  ubuvu  all  thiuun  uvoiil  wcuryiiiu  tln-in  liy 


<-^r  ^:.- 


w 


TKACIIEUS'    MAX  UAL 


rupetition  of  iiiiiiiteroMinji  ulfmcntiiry  work.  They 
liav«!  no  iippreciatioii  of  alwtriic^t  triitli!*,  nor  of  tlic 
words  imeil  to  oxpruss  siicli  trutlia ;  but  tlii'y  ivre  ox- 
»H';-(liii(,'ly»t'n«itivi!  to  visible  forms,  and  readily  acquire 
a  knowledge  of  them.  It  is  posMible  to  reach  their 
uii.lcrstan<lin},'  through  the  heiiae  of  night  sooner  than 
by  appeals  to  either  of  the  other  senses,  or  by  logical 
explanations.  Geometric  accuracy  in  fr"ehanil  or 
model  drawing  is  not  to  he  expected  of  any  one :  the 
standard  by  which  the  efforts  of  little  children  are 
iud^'ed  should,  therefore,  be  a  very  merciful  one. 

I'OWEK    <'l''    onHEIlVATIO>f. 

Since  intelligent  drawing  is  always  an  expression 
.(f  knowledge,  the  power  of  observation  must  be  cul- 
tivated from  the  outset.  Pupils  must  be  trained  to 
discover  the  features  of  whatever  they  are  to  draw 
before  they  begin  their  work.  To  take  a  simple  illus- 
tration :  When  the  pupils  liavo  learned  the  names  of 
the  ditten^nt  straight  lines  and  angles,  the  square  may 
be  given  as  an  exercise.  The  teacher  should  draw  it 
on  the  blackboard,  requiring  the  pupils  to  name  eacn 
lino  as  drawn,  ami,  when  the  figure  is  completed,  to 
give  tlie  number  and  names  of  the  angles  it  contains. 
After  the  diameters  and  diagonals  have  been  drawn, 
tho  pupils  should  then  be  required  to  state  the  effect 
of  these  lines  upon  the  original  angles,  and  to  give 
(he  number  and  Tiames  of  the  new  angles  and  tri- 
angles. Other  exorcises  may  be  treated  in  a  similar 
manner. 


i 


-  -V  V- 


rk.  They 
nor  of  tin' 
ii'V  iire  ox- 
lily  iicquirt' 
:L'iich  llieir 
ooiuT  than 
■  by  logical 
M'oliaiul  or 
y  oiiu :  the 
lildren  iirc 
tl  one. 


exprpssion 
lUst  be  cul- 
I  trained  to 
iH'  to  <lriiw 
iniitle  illii!?- 
e  nanies  of 
square  nmy 
uld  draw  it 

name  eacn 
jmpleted,  to 
it  contains, 
seen  drawn, 
:e  tlie  effect 
mid  to  give 
;h  and  tri- 
n  a  similar 


1 


ISrilOlHIL'TlOS. 


CLASS    ANAIiYSIS    OK     KOIIMS. 


tt 


Wlii'M  the  cards  are  used,  a  class  analysis  of  tin- 
fi^jure  should  frecineiitly  pre- 
cfflf  the  drawinj; ;  that  is,  the 
pupils  should  be  required  to 
describe  the  general  geometri- 
<'al  form  of  the  ligure,  and  the 
vari.ius  lines  wliich  it  contains. 
To  take  card  exeicise  No.  'M 
for  example :  The  analysis 
would  show  the  pupils,  before 
they  bejjau  to  draw,  that  an 
obloii}^  woulil  enclose  the  vase  ;  that  the  vase  is  sym- 
metrically arranged  on  an  a::is,  its  two  sides  being 
alike ;  tiiat  it  is  (imposed  of  conqxnind  curves  and 
horizontal  lines;  that  the  top  and  bottom  have  the 
same  width  ;  that  tlie  widest  part  is  near  the  Imttom  ; 
that  the  narrowest  part  is  the  neck  near  tlie  top ;  thftt 
it  has  abase;  that  the  compound  eurves  make  both 
the  widest  and  narrowest  parts:  that  they  <lo  not 
reach  to  the  bottom ;  that  there  is  no  ornament  on 
the  vase  exce[)t  the  horizontal  lines.  It  will  be  seen 
at  once  tliat  this  prelimiuiiry  analysis  must  develop 
the  observing  powers,  must  iirndy  tix  in  the  mind 
the  i)rinciples  of  drawing  and  design,  must  enable 
the  pupils  to  do  their  work  intelligently. 

First  of  all,  then,  tint  eye  is  to  be  educated  tt> 
distinguish  form,  and  the  mind  to  comprehend  prin- 
ciples: the  correct  .nanual  rendering  of  the  form  is  a 
simple  matter,  which  will  come  by  practice.  In  the 
early  lessons,  therefore,  teachers  should  biy  more  stress 


12 


TEACHERS'  MANUAL. 


iilion  tlevi'lopiiiK  oltsorviition  and  underHtaiiiling  tliiin 
ii()()M  lUciM'  dexterity  in  exocution.  It  in  rare,  almost 
lUHiiduntiil,  for  yoiiMj,'  |)Ui>il.s  to  draw  elear  unbroken 
lines;  wliilo  linos  varying  in  thiekness  must  be  ex- 
lieeted  from  tliem  for  a  long  time.  In  criticising'  tlieir 
etVorts,  form,  irrespective  of  beauty  of  execution, 
should  be  maiidy  considered  at  first.  Wlien  form  has 
bc-en  fairly  masterctl,  then  teacln-rs  nuiy  begin  to 
insist  upon  better  li  .'s  and  more  careful  workman- 
ship.    One  thing  should  thus  be  taken  at  a  time. 

DBAWINQ  0\  THK  HLACKUOAKD. 

Drawing  on  the  blackboard  slu>uld  be  practised  at 
least  once  a  week  by  all  the  pupils;  a  section  working 
on  the  board  every  time  a  lesson  is  given,  th(i 
others  working  at  the  same  time  on  tli.ir  slates.  Vupils 
will  be  deliglited  with  this,  while  it  will  aftbrd  them 
variety  of  practice,  whicli  is  important.  It  will,  in 
particular,  allow  them  to  make  their  drawings  on  a 
large  scale.  This  work  on  the  board  may  be  termed 
the  completest  exemplification  of  freehand  drawing. 

LKNOTH    OF    I-E.SSONS. 

Short  lessons,  often  repeated,  are  better  for  young 
pupils  than  long  ones  at  greater  intervals.     Four  les- 
sons a  week,  of  half  an  hour  each,  or  .six  of  twenty 
minutes  each,  will  bo  a  fair  amount  of  time  for  chil- 
dren under  ten  years  to  give  to  drawing.     After  that 
I     age  the  lessons  may  ho.   longer  and  not  so  frequent, 
!     while  new  subjects  may  be  taken  up.     When  instruc- 
i     tion  is  given  at  all  in  drawing,  the  lessons  should  be 
;     sufticiently  fre(pient  and  sufficiently  long  to  keep  the 


INTIinhnrilDS. 


m 


aiiilin^;  tliiin 
rare,  aliimst, 
ir  unbroken 
iimst  Iv  ox- 
iicisin^;  tlicir 
f  execution, 
len  ioriu  luiH 
ivy  begin  to 
il  worknmn- 
;  a  tinit'. 

ID. 

priictisc'd  at 
tion  working 
i  given,  tho 
kites.  I'upils 
I  aftbrd  tlieni 
.  It  will,  in 
•awings  on  a 
ay  be  ternied 
tid  drawing. 


ter  for  yotmg 
is.  Four  les- 
six  of  twenty 
time  for  ehil- 
;.  After  that 
;  so  frequent, 
kVhen  instruc- 
lona  should  be 
ig  to  keep  tlio 


■%* 


jiupiis  iilivi'  to  tlieir  work,  and  tliomu^'lily  iuleresled. 
Two  Hlioi't  lessons  a  week  will  Mot  do  tliis.  |''our  Irs- 
Bons  will  much  more  than  doui>li'  the  results,  and  six 
lessons  much  more  than  trelile  tlicni.  This  is  not 
only  true  of  drawing;  Imt  every  teacher  who  has  trii-il 
tint  experiment  knows  that  it  is  also  triu*  of  arithme- 
tic or  geography,  for  t.-xample.  In  neither  of  tliese 
studies  wouhl  any  one  expecrt  to  nmke  any  satisfac- 
tory progres.s  with  only  two  short  lessons  a  week. 
Indeed,  the  time  would  i)e  regarded  as,  perhaps,  woim- 
than  wasted;  sini^e  tlie  little  progress  actually  nuide 
would  not  compensate  for  the  disgust  many  of  the 
childrtMi  would  .icipiire  for  the  .study  thu.s  treated.  If, 
then,  drawing  is  to  he  taught  at  all,  it  should  he 
taught  in  earnest,  and  not  as  a  merely  tolerated  study. 
Even  its  decided  attractiveness  will  not  Inlly  compen- 
sate for  the  lack  of  earnest  work. 

Again,  if  any  new  study,  whatever,  is  to  be  put 
into  a  school,  it  .should  receive  for  a  while,  if  possible, 
special  attention,  in  order  to  emphasize  its  importance 
in  the  minds  of  tho  i)upils,  and  to  make  a  strong  he- 
ginning.  To  begin  well  is  half  the  battle.  When 
the  new  study  is  thus  once  firmly  established,  it  may 
then  take  its  place  with  the  other  regular  studies. 
Thus  should  the  schools  welcome  drawing,  which  is 
destined  to  contribute  so  much  towards  the  future 
prosperity  and  culture  of  the  country. 

UrOTATIUN  KXERCISKS. 

It  is  remarkable  how  few  persons  can  accurately 
describe  the  true  form,  size,  proportions,  color,  and 
character  of  any  thing  which  tho  eye  sees.     People 


'    i 


14 


TEAVIIKUS'    M  Ay  UAL 


hiivi-  K'''>i'nil  iinprcssioiiH,  wliidi,  brdii^lit  fo  tlio  ti'Ht 
of  (li'scriptioii,  lire  round  to  In-  vii-^ui'  iiml  alto^rctlicr 
iiiirt'liiililc.  Dntwiiij,',  i>nM'f(lfii  l)y  rriticixm  uimI  uii- 
iiIvkIh  of  copies  or  ohjf.tx,  ill  wliich  Wfll-clioHPii  tiTiim 
(Ifscrilii;  (li'tiiils,  tiiiiiiot  fuil  to  wlticiito  even  tlio 
i<;is.iiiin>;  powers  us  well  us  the  imitutive  and  iirtistio. 
i''oi-  til  is  purpose,  lessons  should  also  lie  freijueiitly 
dictated  by  the  teacher,  without  illustration  in  hooks, 
on  cards,  or  on  the  Idackhoard. 

For  this  kind  o^'  instruction,  artificial  ohjects,  hiiv- 
int;  f^eoniotrio  forms,  are  hetter  suited  than  natural 
ohjects.  For  example,  houses  of  simple  proportions 
may  thus  be  dictated  and  drawn.  When  such  n 
drawing  has  been  executed,  it  is  then  iwlviaiiblo  to 
require  the  pupils  capable  of  doing  so  to  write  a 
minute  descri[)tion  of  it,  giving  its  form,  size,  pro- 
portions, ScK.  There  could  not  possibly  be  a  better 
subject  for  a  composition,  when  it  is  desired  to  teacdi 
exactitude  in  the  use  of  language. 

A  simple  illustration  of  the 
I  dictation  exercise  is  here  given. 
I  The  drawing  of  the  annexed 
geometrical  form   may  be  «lic- 
tated   thus :    Draw    a   square, 
jits   diameters    and   diagonals. 
Halve    the    semi  -  diameters. 
I  From     each     corner    of    the 
iquare,  draw  a  straight  line  to 
I  the  nearest  point  of  division  on 
each  diameter.     Un  the  diameters  of  the  lirst  wpiare, 
as  diagonals,  draw  a  second  .s(piare.     Erase  the  diago- 
nals of  the  first  square,  and  the  outer  divisions  of  its 


^ 


lyriuiinvnas. 


15 


t  fo  tlin  text. 
(1  iiltD^jctlicr 
iMiii  iiinl  uii- 
L'lioHOii  torniH 
;i!  even  tlio 
1111(1  iirtiHtic. 
«  fri'iniriitly 
ion  in  bnokx, 

<il)jpct»,  liiiv- 
thiiti  niitiiriil 
>.  proportionH 
lien    such    \\ 

lulvitiiiblo  to 
D  to  writo  II 
m,  Hizo,  jiro- 

lic  n  better 
lired  to  teiKili 

ration  of"  tlio 
islinre  given, 
tlip  iiiinexe<l 
may  be  <lie- 
iw  11  (tquiire, 
id  diitK(»»i1>*- 
li  -  diiuneterH. 
rner  of  tlu) 
;raight  lino  to 
of  division  on 
e  lirMt  s(Hiart', 
use  tlic  diago- 
iviaioiirt  of  it« 


ft 


diameters;  also  tlume  purtM  of  tlie  inni-r  hcjiiari'  wliicli 
K<>  beliind  the  poiiitK  of  tlio  star.  If  tlie  pupils  lieed 
what  is  dictated,  they  will  pnMlu.x'  the  re.piir.,!  |ij,„re  ; 
if  not,  tiioy  will  draw  HomethiiiK  else.  After  the 
pupils  have  finished  their  work,  the  teii.;Iier  will  draw* 
tlio  llf,'iiro  eorreetly  on  tlio  bla(lti)Oiird. 

Tho  object,  then,  of  dictation  exercises  is  to  mIiow 
that  forms  and  words  nre  interehanpablo,  both  being 
niediuins  for  tho  expression  of  thought;  to  teach 
IHipils  to  lis.)  either  language  with  equal  facility;  to 
translate  and  retranslato  ♦rom  one  into  tin;  other. 
Such  exorcises,  beginning  with  siniplo  geomutric 
forms,  may  bo  continued,  until  th.)  most  •■laborato 
irregular  forms  can  bo  drawn  from  dictation,  if  tho 
language  describing  them  lui  nceunito  and  terse. 
Artisans  have  constant  use  for  the  j)ower  which  is 
m-quired  from  dictation  exorcises. 

MKMOKY  KXKHCISKS. 

J'upils  sIxMild   bo    frequently  required  to  produce, 
from  memory,  exercises  which  tliey  have  previously 
drawn.      This  will  show  tho  tea.her  how  much  of 
previous  instruction  is  retained,  while  it  is  valuable 
simply  us    a   means    for    developing    the    power   of 
memory.     Therefore,  as  soon   as  pupils  have  got    a 
limited    knowledge  of   forms,  they  should  begin  to 
reproduce  these  forms  without  sofcing  the  copies  and 
witliin  a  specified  time.     It  is  also  urged  that  the 
pupils,  leaving  their  cards  at   school,  b<!  occasionally 
required  to  do  their  drawing  exercises  at  home,  from 
raemorv,  and,  putting  them  into  i.  little  book  provided 
forthu  purpose,  bring  them  to  the  te-idior  forinspection. 


\(\ 


TKACIIKU>''   MASUAL. 


IHI.INU    AM>    MKAXUUISa  ( 

With  ea<li  Hoiifn  of  ••iirds  there  \h  a  tlvo-iiu-h  m-nU',     , 

the  iiuhcH  (liviilfii  into  halves,  .iiiiirt.T«,  iiml  sixt.-.-iitli-.     | 

Thirt  sciil.'  shoul.l  Ix'  usf'l  (inly  fur  (i.nv.tinj;  lin.-s  iilt.T 

tl.ry  hiive  hiMMi  .Iniwn,  iin.l  u..t  to  hi-lj)  in  tir.-t  (iriiwiiiK 

tlM-Hn«'s.     TciichcrH  must  H.T  that   pupils  tlo  not  .w 

tiu>  Hciih'  ill  tho  niiini..'    prol.il.it.a.     It  i«  cHHiiliiil 

tliivt  tl..-  first  liufs  of  any  .iriiwint,'  should  h-  iipproxi- 

Miatcly  oornct,  otlu-rsviso  tin*  ninainiuK  liiu-s  will  h.- 

wli.illy  out  of  phu-c.     Hnii-...  wh.^n  tli.'  iirst  propor- 

tiuuui   linos  have   In-t-n    drawn   as    n.arly  .orrf.t   as 

possible  by  the  oy.'  alon.-,  pupils  shoul.l  U-  p.rniittfd 

to  m.-asure  th.-ni,  and  to  .orrcct  th.MU   if  th.-y  ni-cd 

corn-ction.     Ft   is  to  l.o  distinctly  undt-rstood,  how-- 

cver,  that  the  ninasurin.i,'  is  not  to  1...  porniitlnl  until 

the  lines  have  been  <lrawn. 

Some  teaduTS  say,  "  N.-vr  draw   a  straight  lino 
freehand  if  you  hrve  the  means  of  ruling  it;"  yt 
it  is  better  thus  to  draw  straight  lines  than  to  rule 
them,  unless  it  is  absolutely  essential,  for  some  speenil 
reason,  that   they  he    mathemati.'aily  straight,  both 
because  it   is   good    J.racti..!    for  th.;  eye  and  hand, 
and  mak.'S  the   pupil    in.h'pendent  of  ruler...     Th." 
name  mav  he  said    of   drawing   eireles.     Of  course, 
when  any  thing  of  in.portanee  d.-pends  upon  a  curie 
bring    perfe.tlv  drawn,  it  is  hest  to  use  a  pair  ot 
..ompas.ses;    but    a   circle    practically  exact    may  he 
.Irawn  fr.'ehand  with  very  little  experience,  and  it  is 
,.du.:ational  thus  to  draw  it.     In   practice,  it  will  ho 
found  more  diflicult  to  rule  ."ith.  r  vertical  or  horizontal 
straight  lines,  than  to  draw  thti-i  by  the  aid  of  the 


111  Hixtc)>iitli!«. 
nn  liiii'»*  at'tt'r 
tir^t  (Iniwiiij,' 

iirt  do  not   iis«> 

t     \h    ('M><'lltitll 

III  lit'  iipiirnxi- 
liiics  will  Ix' 
■  iirst  propor- 
rly  I'on'fi't  iw 
I  lif  pcrmittfil 
if  tiny  lU't'tl 
Icrstiioil,  liow- 
I'l-iuitli'il  until 

fc  Htiiiinlit  lino 
ilinn  it;"  y«'t 
(  than  to  rule 
>r  sonu)  upciMiil 
strai^lit,  biitli 
>yo  ami  hiind, 
f   ruler.       Tlif 

H.       Of    COUISI', 

,s  upon  a  irirrli! 
uso  a  i>air  of 
cxiift  nuiy  1)1! 
ieiici',  anil  it  is 
^tico,  it  will  Iju 
ill  orliorizontal 
the  aid  of  the 


ISTIlOlilrnnS. 


IT 


<•>'»'  illoiic  A  Hoini'wiiat  fxlfnilfd  i-xpiTiiMioc  in  trurli- 
iii^,  witli  riiiitinui'il  olisii'vation  of  (In-  work  of  niuny 
piipiU,  has  niiiviiici'd  th<>  author  that  thoHc  win* 
draw  viTliiai  and  horizontal  lint's  frcidntnd,  lH>>idi*s 
doinn  thi'ir  work  in  h'-s  time.  ;,'i'ni'rally  tnakr  their 
lines  ninif  iieiuly  ii|pri^;hl  und  level  than  tlM»e 
who  rule  iheiii.  Tho^e  only  draw  well  wlm  draw  in- 
teliij^ently. 

I'owiritiN. 

When  vertical  and  hori/.ontal  lines  iin-  drawn,  the 
slate  iir  paper  shouhl  be  k.  pt  in  one  position  in  front 
of  the  piijiil,  its  fdgu  paralhd  with  tho  ed^o  id'  tint 
de^k.  When  ohliipio  lines  uro  drawn,  the  slate  or 
paper  may  he  kej)t  in  the  Hanie  position,  while  the  hand 
is  turnt'd  so  that  the  vision  may  not  bo  oh.structed. 
When  cu-V(;s  aro  drawn,  it  will  he  bi-st  to  allow  the 
slaN!  or  paper  to  he  put  in  any  position  the  pupil  may 
prefer,  in  order  that  the  hand  nniy  form  the  eentre 
of  tho  c!urve  drawn,  which  can  be,  in  fionn-  cases,  only 
when  the  drawing  is  turned  sidcwise  or  upside  down. 

l'Ky«'lLS    AND    MUUKIS. 

The  slatu  punciJH  should  be  soft,  lonij,  wtdl-pointed, 
and  held  about  an  incli  and  a  half  from  the  eiul,  far 
enough  to  keep  the  lingers  from  obstructing  tho  vision. 

For  tho  purpose  of  illu.strating  many  of  the  ex- 
orcises, and  accelerating  the  advance  of  tho  pujiils, 
••very  primary  school  should  have  a  box  of  models, 
which  can  be  procured  of  the  publishers  of  this 
book.  /  Such  a  box  would  contain  a  sphere,  cube, 
oblongV  block,    triangular    prism,    hexagonal    prism. 


tit 


niM'IIKRS'    MANUAL 


...,iir,   ,y\mU%  r.-tim«iiliir  i.yruini.l.   ^<iu.if«'    Imiius 
I'lDn^,  itt.il  Komo  otlhT  pi H.         ^ 

III  ....iMlii^iMii,  til.'  imtlior  wnuM  -ay  that  tin-  .InM 
^slm.lrasvH  tV-.n,  liv.-  y.-ar^  .-f  a^.-  U,  lilt.-.-n  -n^l.t  t- 
1...  al.lr  t..  .Imw  u.iy  .•r.Mit.-.l  tiling',  uiwl  will  I-  ai.l.' 
to  a..  HO  wl.-..  vvv  U'lxch  w..li  wl.at  .■v.-ry  rl.il.l  n„«l.t  t,> 
know  Tln'iv  irt  no  royal  roii.l  to  .liawinn  :  an.l  tliosf 
wl...  i.rofV..H  t..  otV.T  Hu.h  a  roiul  to  u.  umy  l...  h.im 
,„...f.-l  of  a  .K-mro  to  iniHlt-ml  with  a  r-Kal  J.unii"  wliiH. 
iv|iri'«outH  nothing. 


I 


,. 


L.-- 


iImi 


tnn*    tViiiiit', 


III  ilif  .liiM 

I'll   iill^llt    !<• 

will  I"'  iil'l'' 
lilil  iiii({lit  to 
;    iillil  tlliiHi- 

limy  !••'  »"•*'* 
iiiiini'  vvhii'h 


■ 


<'IIAITi:U    1. 

CKNTUK,   POINTS,    AM)   STHAIOIIT   f.INKS 

Wiii;\  yomiK  cliil.ln'ii  \>rff\u  to  dniw,  ti'iiih  ili. m, 
(ii>f,  tlic   nu'iiiiiii^  (if   till'  wiinl   'ii'iitiv."     l:ri|iiiri' 

tliiiii.  I»y  wiiy  lit'  illiiMfniti to  tmiili   tl ihtn-  .'I' 

flii'ir  n\nU>A   with    tlii'   iihI    of    tlirir   iiciicIN,     Tliis 
ii'iitri'  we  will  call  ii  point. 

A  Point. 

A  /»>!nf  h  slm/ttji  jinsithiii  III- /,forf,  in'thmtf  shi; 
iiiiil  iiiai/  hi:  tiiiliiati'il  In  ifi(l'nriif  irni/s. 

Kxiiliiiii.  next,  til.'  iiii'aiiiiiK  of  tlic  wmds  ••  ri>,'Iif  " 
mill  "  li.ft.''  Diiiw  ii  v.'iti.iil  line  on  tin'  l.|ii.klioar.l ; 
t<i  till'  ri^iUt  of  this  line  draw  iinothcr.  i'\|ilainiin,'  that 
till'  last  is  to  the  riKht  hand  of  tlii'  (iist.  In  tlm 
Manii'  way  illiisinit.'  tin-  nifaninj,'  of  tin-  word  "  l.-fr." 
Next,  draw  a  horizontal  I'lif,  and  in  a  similar  inanni'r 
••xplain  till'  iiii'aniiijr  of  tlm  words  "  al.ov.',"  '•  h.'low." 

Always  niakf  tn-rtain,  in  sonit-  way.  that  ihildrcn 
havi'  a  oli'tir  undi'rstandinj,'  of  wliatrvi-r  is  used  fnr 
the   iHiritoHo  of   further  extending,'  their   knowledK... 

It  is  well  to  tak tiling  for  planted.  \kH  tn  e\|.laiii 

the  simplest  things.      When  the  eelehrafed   Faraday 
leeturi-'d  heforo  ehildren  at  the   Royal   Institute,  Loii- 

'' h«' was  neenstonied  to  illustrate  the  most  common 

plieiiomena.     He  would  not  take  it  for  granted  that 
the  children  knew  that  an  apple,  when  unsupported, 


Ji« 


TKU'llKliS'   it  A  SI!  Aim 


will  liill  t«  ''"•  ur.iiiii.li  I'lit  li.'  wi»nl«l  w'UmWy  llliin- 

4ri(AI<llll'    LINK*. 

.V  VkUTUJAI-  lilNK.  —  .1  verfinil 
liin  U  a  Hinilijht  lim',  wh'nh  f»nn  lift 
mill  iloii'ii,  iiiiliiiinij  in'iHnf  In  /An 
rlijlit   imr  l»  flf  I'jl,  »"«'/«/•  A'"'** 

ll'ill-'ll  llitl'  Joiii'iii'iIh    (lit. 

A  ll..uizi»NT.v;,  Link,  —  .1  li"ri::'»if'il  li,,.-  m  ./ 

I.,',  I  Hfml>)ht  lliif,  iiflhihitf  ni'il/>.r  ii/>  »'»• '/""/'  d')- 

An  Oiii.Kii'K  Link.  — .1/'  »/,li</iir  liif  is  ,i  Mh-nifflil 

/i,„;     iinithrr    I'lii'linil    nor    lionxmiln/,    Inif     hI.u.I- 

i'l'.l  <'■)•  ,.  ,11 

Kii-Ht,  ilriiw  til"  tliiTi'  UwU  oj  lihi'H  Mil  til..  iM.anl. 

iiii.l  ^^\v>'  tlHMr  luiiiu'H.     Tiu'U  rf<|uiro  tli.-  i.ii|.iU  ti» 

,liaw   tl I    "„    tli.'ir   HliU.'r4.   witliniif    ttiniiim    tli.ir 

>liit-H.  Ku.'li  liiM-  NJKml.l  Im(  tlr.iwM  nmnv  rwuv. 
until  th..  iMijiilrt  can  im*tunlly  .li«tiii>{iii.'li  l.-tw-.n 
tl,..  ,litV.T.'iit  liii.'rt;  until  tlioy  riiii  ii.Hiuntly  \now 
tlirin  wli.'ii  «lniwii  l>.v  til..  tfiidiiT,  or  iiiMtiintly  .In.w 
tin-Ill  wli.-ii  i.uni.'.l  hy  llu'  tfurli.-r.  A  Htniinlit  Hli'U 
lifl.l  in  .lilV.'Vi'iit  piisitioiif.  will  Horvf  riift-ly  to  illiii*- 
tmt.!  th."  mi'iiiiiiiK  of  tli<»  wonN  "  liorizmitiil,"  "  v<-r- 
ticiil."  "  ohii.iu.-."  UcqiU'st  til.'  pupils  to  ii.tni.i  ohj.'ct. 
ill  tli.'si"  iimVr.'iit  positioiiH. 

V.ui\UUKUlASKn.—l''n-alM  Utirs  am  lin>n  run- 
nlii'f  nt,h,  I'll  shir  III  til,'  nam:  dirrrtioii,  ami  arr 
nhr.f/s  lit  tl„-  mnw  distann;  from,  our  another 
thron.jhoat  thr.lr  wholr.  Imijth.  Thr,,  moij  Im  Htraijht 
or  r.armd,  tnrtial,  ohliqur,  or  horixontal. 


uritAiuin  usfis. 


it 


imll)  illiin- 


.1    I'i'ffiiiit 
lih  rinm  Uf> 

ffirr    f»    till' 

•iiliii'  bni'k' 


il   liiir   i.i    II 
II'  iliiini  ( II). 

is  II   Mfl'llil/llf 
llllt       Hlill.t- 

II  till'  lioaril. 
Iit>  |iii|iiU  to 
iriiihu  tluir 
iiaiiv  tiiiii", 
iii|i   lictvvi'i'ii 

tUlltlv     lllUlli* 

wtiiiilly  'Iniw 
tnii>?lit  *U'\< 
ci'ly  ti>  illuK- 
iiitiil,"  "  v<'r- 
iiitiiiii  object* 

re  lini'n  run- 
ioii,  and  arn 
mil'  another 
III/  liif  sfruiijht 
il. 


. 


iJrtw  Mil  flu-  iMiufl  |>iinillfl  Virtual  (.\»,  lu'ri/oiiiil 
ltd,  aiiil  ••liiii|iii*  liiii'"  (<!.  liixl  ri'i|iiiri' 
llix  |tu|>ilM  to  ri'iHiit  tliciii  nil  tlu'ir 
ttluti'H,  witlimit  liiriiliiK  tlii-ir  MJalt'D. 
Tliix  il*  Hii  I'stTiim-  111  wliiili  yo'i 
nIhiiiIiI   trii|Uiiitly    ii'Vi-rt.      WIm'Ii    tin-  ^ 

|Mi|iil«   liavii  ilrawM   Iwn  liiii'i*   |iaritllcl,  rcquirk)  tln-in 
to  <lra\v  Ik  tliini  ill   tin'  niitri'  liftwiin 

till*    two,    IIIkI     tllllH     ill     tlll'lll    illtltllllli' 

to  lialvf  till-  diiaii'H  liitwi'i'ii  till'  liiu'f'. 

until  tlif  liiii'H  uri' very  «*|ii-i'  tii)Xi'tlH>r. 

Till'  pfiKil  xlimilil  liitv.'  u  Hill'  |niiiit 
I'l-r  thi*  \v.irl<.  ami  im  two  lini'*  mIi"|||i|  Ih'  all'.rMd  t<i 
tomli  I'luli  otIiiT.  TliiH  Im  I'xri-lli'iit 
|irii<'tii!».  An  Moon  III*  tlii>  |iii|iiU  liavi' 
ui'i|iiira<l  winif  hUIII  in  jiulKiii;{  'li"*- 
taiiicH,  if.|iiiri'  til. 'Ill  t<i  'Iraw  parai- 
It'l  litioM  nl'  ili'linitf  li'ii^tli,  UM  mil' 

illl'll,    two     illclll'H,     X'l'. 

I'miiU  >*li.iiilil  have  a  tliar  imiliTHtaiuliii;^  of  paral- 
li'l  lini'x.  'riii'ri-  iiri'  two  tliiiin^  ri'i|uiwiti'  to  mukf 
litii'!*  paniilil :  tliry  niiiKt  lie  niile  liy  niili',  ami  tln-y 
tiiiiKt  liavc  till-  HaiiK-  tliii'i'tioii.  U'lim,  llH'iit'orf.  u" 
want  two  parallel  vertical,  or  two  parallel  liori/.iiiital 
liiu'H,  it  i>t  not  eiiou;»li  to  say.  "Hraw  two  Mitiial 
liin'rt,"  or.  "  Draw  two  liori/.ontal  line'.;  "  lor  in  iieitlur 
ease  lieetl  tile  lilies  lie  drawn  side  liv  side.  Nor  is  it 
eiioiiuli  when  two  purallel  lines  are  wanted,  -imply  to 
draw  tlu'iu  tiidt'  by  aide;  for  niile  bv  siib'  diM,  not 
neeessarily  mean  tliat  tlie  lines  must  liave  e\aetly 
tlie  same  dire'-tion.  Ileiiee  we  must  >iiy  parallel  vei- 
tietil  lines,  parullel  perpendienlar  lines,  parallel  oblitpie 


n 


rKAVllHHH'  MAM'U. 


tth*>«.  or  |M»riitt«-l  tM»ri»><>i)ftil  tttM>«,  un  ttii>  ••na«>  M>i»y  U-, 
If  Wf  wniM  •!»)  |(i«t  »liiii  wi'  iiM'iiii,  A»  ItirtlM-r 
|)t)>Krt>*«  !•  iHinlf  ill  Itii*  •••Hir«i*  of  ilnmhiti,  it  will  U' 
iiioro  I'ti'iiilv  ••'•>•  wli.v  ■••  MiiU'li  MlrvM  (m  i  '  "inmi  tbi* 
••xiifl  II"'  "f  tirni*. 

Hfi'  ihiil  'III'  |Mi|)iU  iiIhuv*  linvc  lutt^  iiimI  ut'll- 
|i'>iiit)>i|  |i»>ni'tU;  tliry  i)liuiilt|  iii'vcr  \m  uIIhwimI  in  ilniMr 

««llll  nllllxi  >)|-    hllllll    iM'lh'iU,       To    iMiltti'    xlll'i'  lllitt   till* 

|>'  iK'il*  iin*  iihviivt  III  ^ihhI  I'oiiilitiiih,  kri'|i  tin  III  in  ii 
l>'>\   iiiiiji'r  yiHir  Murii  iliiirui'.  ii»  \>*'  ilinrriltiiicil  uml 

litki'll    )l|l   lit  V\fr\    It'iKitM,       .\|(|Hlill|    Ktiliii-   IMM-  i)f  |Ih> 

|Mi|)il«,  t'riMii  ilitv  >••  *liiy.  tti  »liiii|M'h  lIn'  |m'I|i  iln,  it>>iittt 

till'    tVt>rk    uIm'Ii'    it    will    l|i>l    lll-tlllll    till'    '•r  lliloj,         N\   lt||> 

iHit  uinnI  iiiiiti-riitl)  it  U  iiii|Hm>iili|i'  to  ijniu  ra|)ii|lv  iiimI 
w.ll, 
•      Till'  |M'iii'il  >liiiiili|  III'  III M  aliiiiit  ail  iiH  li  iiitil  It  liall 
I'l'iilll   til)'    |liiitlt,  iMhI    no    Ik  III    tllllt    the    lliilnl  will    lint 

I'tMih*  lintwiMMi  till'  vyi'  iiiiil  tliM  K|mi'i<  ulii'i'i'  tlir  lint*  U 
III  li>'  ili'awii.  iilMtriii'liiiu  till'  vi'iiiii. 

Wlii'ii  ili-ii\viii}i  •tr.iinlii  iitii'o  III  ilirti'i'i'iit  liiivrtioiin, 
iii«  liori/oiitjil,  vrrtii'tkl,  itml  iil>lii|iii'.  iii»ti>ui|  nntii'iiiii^ 
till'  xluti'  III-  |iiiiii'i'.  turn  till'  liiiml,  OIwitvi'  tlii">i'  two 
tliiiii^i:  t'hvuvM  ki'i'p  till- liiuiil  jiihI  IIii^ii'm  in  ii  |Hi«i- 
timi  of  I'ri'riliiiii }    iii'Vi'i'  lit   till'   liaml   obitruit    tlin 

hiu'lt. 

Itiiiw  till'  Hliort('«r  liin  '  witli  tin*  Pn-'frx  itmii't 
ilniHi'  •iiiini'wiiir  '  •  ;•  1  It.i  with  tin-  ii.iinl,  lifting  the 
\»ri'.t  joint;  tin*  iii'xt  j^nuli'  ilniw  wifli  tlu'  lori-uriii, 
iiiii'i  till'  I'lliow  jiiiiit ;  tliiw  lonj^i'i*  yi't,  wliirli  will 
ii'«imll,v  III'  oil  fill'  liliii'Uliimnl.  ilniw  with  tin-  wlmlw 
arm.  ii^iir,'  tin-  ■*1iimiIc1i  r  jciinf,  <  ►iTu-iinnallv.  in  iliaw- 
iii','  a  ^''t'V  \»\t>fi  liori/oiital  liin'  i>ii  tin-  lilai'ltliiianl.  it 


•  «• 


HTH  tin  HI'  /./,V>i* 


Uil 


A«  liirfltcr 
»)(.  it  will  U' 
fi!.'  "|Hih  llif 

m    IIIdI    Hi'll* 

>wi'<|  |i»  ilriMV 
•nil  lliitt  llii> 
|i  tin  til  in  II 
irilxiii'tl  uimI 
••  UIM*  nf  |Im> 

••iii'iN,  )titiiiix 
I'tiil,  \\  ifli« 
'  rit|*i)ll,v  iiimI 

li  mill  It  liall 
iiM>l  will  init 
Ir  till'  lint'  \n 

It  iliivi'lioiiK, 
111  ol'  hii'iiiii^ 
VI'  till'*!'  two 
X  ill  II  |iii«i. 
*l)ttrii)'t    till- 

I'.'i'r-*  iImim'  ! 
III.  lining  tin- 
Ill'  liiri'-uriii. 
.  wlii.li  will 
li  till-  uIimIi- 
illy,  ill  liniw- 
liii-kliiiiii'<l.  it 


U  It ••nr>  to  I'lirry  lit"  IhhIv  f^^t\^^m\  it>  IIm'  Hiu'  i<* 

•Iniuii.  Ii  i<  iN->i,  wlii'it  ilmwiiiu  ti  vi'rtb'iil  Uiit*  on 
till'  ^t|,t••kl•^M^^I,  ••»  •IihuI  tlini'tly  in  rrniil  .if  wln-rt-  •Iim 
IliM-  K  III  Ih-  ilrtwh.  uiili  till'  >lit>'  |iiirti.klly  turiitit 
iin»itr'U  (In-  In'UkI.  uii'l  dir  i-inniuli  uwuy  '■'  '•''  •'"' 
liiiii'l,  wltiti  till'  iiriii  io  i-kti'iiilitl.  fitll  I'Huilv  i-.trr>iitt{ 
»liM  rruyoii  iliiwii.  N'l-vtr  ilmw  ti  liitf  with  ii  ,i''rky 
iiMiviiiM  lit,  liiit  iilwiiy»  with  Ik  iiiiitxi'iii  iii"ti"ii.  iii-'l 
•  litw  i'iiiMi((li  t->r  till'  t-yi'  til  I'l'lliiw. 

IMVUll.M.      »IU.\ll.ar      I.INKt     A.Mi      -M.IM.IM.      Ill** 
\hn\\      I'll     ill'       lilllI'MiiMII'l     II    MIIMill 

Iim- 1 1;,   iiinl    iliviili'  it    iiitu  t» |n:ii 

piirtN.  Kxpliiiii  tliiit  till'  ili'iiliiiK  iiiiuk 
>*  ill  tin-  I'l'iitrii  111'  till'  Iim*.  Iliaw  itii- 
•itlnr  litii*  i'Jh  iiikI  iliviili'  it  into  iiiiii 
■  ■'|iiiil  iiuil";  llr-t.  l-y  'livi-Iinu  it  iii'n 
two  i>i|iiiil  {iiii'to,  iiinl  llii'ii  I'lii  h  "I  iIk' 
lialvi>>«  into  twii  )itlii>ri'i|iiiti  |iui-tx.  Ilriiw 
iinollii'i-  Iim-  (.'ti.  ami  iliviili'  it  into  tliri-u  t>i|iiul  |iiii-u. 
Miviilin;;  a  Iim-  into  tlii-i'  ri|iiiil  piirt-*  i^*  nior<'  ilillii'iilt 
than  iliMiliiiif  it  into  two  ri|ii:il  |>art^.  I>raw  aiiotlu'r 
Iim*  (4).  mill  iliviili-  it  into  Hi\  i>i|iiai  paitM  ;  llmt,  liy 
-liviiljn^  it  into  two  i>i|iiai  pail*,  ami  linn  i-aili  ot' 
I  ill'  lialvi--  into  tliii-f  i"pial  pail-.  Wliilf  tin-  ttailn-r 
ilraWH  tln-Ni-  lini'M  on  tin-  Itlai-klioavil,  tin-  |iiipil<«  ilioiilil 
iliMW  iini'H  ol'  a  nivi'ii  |i-nutli  on  tln-ir  «l:iti-N,  ami 
-liviili-  llii-ni  into  lialvi-1.  i|iiai'ti-i--«,  tliinU.  ami  r^ivtlnt, 
follow  iii^' till- li-aflii'f.       lAai'tni-H-*  in  tin-  ilivi-<ioii  of 

lim-it   hIioiiIiI   not   In-  i-x| ti'-l   on   tin'  pint   of  yoiinj; 

|iii[ii|s  at  llrnt,      It   i-  siiHicit-nt,  if  iIh'V  ',"t  iIm-  iili-u. 


24 


THA  fimm'   it  A  NUA  I.. 


.\i:(!ili!iiy  will  I'Dinc  hy  practice.  Tn  tlicxc  ciiily 
.sti.;;i's,  |n'iiiiil  lilt'  ['UiiiU  to  correct  tiicir  t'uiilts  in  t'rcf 
iiic;i<ii 'I'lnciit  l)y  tilt!  iiiil  of  tli(^  scale  wliicii  iiccom- 
|i:iiiicrt  fucli  series  ')t'  cards.  'I'liis  practice  will  lie 
liniiid  tilt)  surest  way  ol"  educatiiif?  tliem  to  correct 
iiliservatiori.  IJefore  resortin^j.  Imwever,  to  tlie  iimi 
(if  the  scale,  the  pupils  should  do  their  hest  with  tlieir 
I'yes  alone.  Drawin}^  and  dividing;  lines  in  this  man- 
ner should  lie  ptactised  in  conniMtion  with  other  les- 
sons, until  pupils  actpiin;  iK^onsideralile  degr(!(>  of  .skill 
in  determining  deUiiito  distances  and  [iroportions. 

Youiifj;  childr(!ii,  unless  they  have  recoivod  posit-ve 
instruction,  seldom  have  any  clear  idea  of  tlie  length 
of  an  inch,  a  foot,  a  yard,  or  mile,  though  they  may 
have  heard  the  words  used  liundreds  of  times.  If 
(plestioned,  they  fretpUMitly  give  answers  that  astonish 
the  (pn'stioner. 

Suppose,  furtiier,  that  it  is  retpiired  to  draw  a  line, 
lint  of  no  particular  length,  and  to  divide  it  into  five, 
seven,  eiuveii,  thirteen,  or  any  other  prime  numher  of 
equal  parts.  In  that  case,  having  drawn  a  line, 
divide  it  into  fouretpial  [tarts,  and  then  add  one  pait, 
to  make  five  ;  or  divide  it  into  eight  equal  parts,  and 
then  erase  oiio,  heaving  seven,  if  that  is  the  iiumlier 
retpiired.  That  is,  first  draw  a  lino,  and  divide  it 
into  a  composite  numher  of  parts,  then  add  or  erase, 
as  may  lie  required.  Th.is  is  not,  of  course,  a  suitable 
exercise  for  the  youngest  pupils. 

Frequently  iisk  the  jnipils  how  they  would  procei'd 
to  divide  a  line  into  any  dosignatcid  number  of  equal 
parts.  If,  for  example,  the  number  is  six,  the  answer 
should   be:    Divide   the    line  into    two    etpial    parts; 


IK 


i 


tile.'*!'     cill'Iv 

iuilts  in  f'ri'i' 

llicil    UCIIDIII- 

tifc  will   ill' 

I  to  I'l.irrcct 

ll>     tllC     I1M< 

it  with  llii'ir 

II  this  iiiiiii- 
h  other  Ics- 
prci'  of  .-kill 
tortious, 
voil  posit'vc 
[■  tlio  length 
h  they  nmy 
f  times.  If 
hilt  iistoiiish 

(Iriiw  a  line, 
it  into  five. 
1!  number  of 
,wn  ii  line. 
M  one  pait. 
il  parts,  and 
the  iiiimher 
1(1  divide  it 
,(ld  or  erase, 
L',  a  suitable 

uld   proeeed 

ber  of  (Mjual 

the  answer 

(|ual    parts ; 


sn/Aiaiir  7./,va..v.  -» 

then  divide  eiuli  part   int..   three   e(iMal    parts,   j,'"^'"^ 

MX. 

foMIIIMM)   STUAIlilir    1.IM:.S. A>I<il,l>. 

As  soon  as  the  pupils  have  anpiired 
a  knowledge  of  straight  lim's,  tiiey 
should  begin  to  eoiul.ine  them.  Draw 
on  the  l>laekboard  a  vertical  line  of 
delinitt^  length,  say  twelve  inehes.  and  ^  u. 
then  reipiire  the  pupils  to  draw  a  similar  line,  say  lour 
inehes  long,  on  their  slates. 

At  this  stage,  tho  linos  should  all  be  drawn  of 
definite  lengths.  Having  first  been  drawn  by  the 
aid  of  the  eye  ahuie,  they  should  afterwards  all  be 
e.orreeted  by  the  seale.  Such  practieo  is  tho  begin- 
ning of  the  study  of  jn-oportion. 

Having  drawn  the  vertieal  line,  next  draw  a  hori- 
zontal line  of  the  same  leiigtli ;  draw  it  from  the 
lower  end  and  to  the  right  of  the  vortical  line.  The 
two  linos,  thus  united,  form  what  ehildren  will  eall  a 
corner,  but  \\iiat  we  will  eall  an  angle.  This  j.ar- 
tieular  angle  (l>)  is  culled  a  right  anglo,  not,  hr.w- 
ever,  beeauso  it  ojtens  to  the  right. 

Bight  Angles. 

A  riff  fit  nnrj/r  /.s'  furmfi  f>i/  thi-  wi'iflu;/  of  fii'o 
Hfvnyjlit,  or  ritj/it,  flncK  j>nrj>cii<llrit/ar  to  I'Uih  other. 

The  pupils  should  be  taught  to  distinguish  clearly 
between  a  vertical  line  and  a  perpendicular  lino.  A 
vertical  line  is  always  perpentlicular;  but  a  perjten- 
dieular  lino  is  not  always  vortical.  One  liiu-  is  said 
to  bo  perpondicidar  to  another  line  when  the  two 
meet   so  as  to  form  a  scpiare  corner,  or  right  angle ; 


2«5 


TKAL'llKliS'   M.iMM. 


yri  linili  lines,  wIiiMi  I'dnsiilcrfil  wifli  ri'fi-ri'iM'i'  to 
\\\vw  |M>.>itinii.  iiiiiy  111-  <>lili(|iic,  Itiit  one  line  is  ncv"  r 
s ml  to  lie  viTtii'iil  to  uiiDtliiT.      U'licii  ji  rl^lit  iinglc 

'!■'•<  1 II    l'"i'i I  oil   ii  sl.itc  l»y  tlic  mci'tiiig  of  !i  vcr- 

lii'iil  liiiM  ;iimI  ii  Inirizoiiliil  line,  it  will  rciiijiin  ii  ri},'lit 
!m^'l(■,  l|ioiii;Ji  I  III.  sliitK  1h(  piirfly  tunicil  nroiind.  ami 
ilii'  lines  ln'coine  oMi(|Mc.  Wlieii  11  Unite  is  liaif 
opi'ii.  it   forms  u  ri'^ht   im^'le  :    the  l)liii|e  is   iiei'iien- 

(iirliliil-  to  tlie  lliillille,  in  wlmtever  Jiosition  tile  knife 
liMiy  lie  lield.  while  llie  liiuiille  is  |>cr|icii<licular  to  tlie 
Maile,  Fre(|iiently  illustrate  tliis  ini[iortaiit  <li.-tiiic- 
tion  hetweeu  tile  Words  verti(Mil  and  iieriM'iwlieuliir. 
mid  always  insist  upon  tlio  pupils  using  tlie  words 
eorrectlv. 

Now  extend  the  liorizontal  line  in  l) 
the  siuiie  (listain'e  to  the  left  of  the  verti- 
cal line  already  ilrawn.  and  explain  that 
the  eornerfhus  fiu-uied  on  tiie  left  is  also 
a  ri^'ht  aui,'le.  Hy  next  extendin;,'  the 
vertical  line  the  sauH!  distance  lielow  the  horizontal 
liiu',  two  more  rij,'ht  aiij;lea  will  he  formed;  and  yon 
will  have  four  ri,t,dit  an^Mes  nn'otiuy  in  a  point,  or  at 
the  centre,  us  K. 

The  size  of  an  aufjle  does  not  dej)cnd  at  all  on  the 
lenjjth  of  the  lines  forming,'  it;  for 

An  iniijli'  Is  f/ir  ififffmirf  In  f/ir  illrrctlnn  itffiri)  lliivs 
ii'lilrli  iiifft.  Ill'  ii'niilil  iiirrf  If'  c.rfnii/ri/  fur  iiidihiIi. 

Tlieref  ire.  the  four  angles  meeting  in  M  would  he 
no  laiLfer,  ihoiitrh  the  lines  were  drawn  lonj^'er. 

l)iaw  rii^lit  anjjles  on  the  hoard  in  various  ways. 
Thus,  draw  a  horizontal  line;  fr<pm  its  left  end.  draw 
a  verticiil  liii'  downwards.      AuMiii.  draw  a  horizontal 


r 


n'Ci'ri'hri'  to 
line  is  iicvi'i' 
k  rij^lit  iiii^lc 
iii^  of  a  vcr- 
iiiiiiii  ii  ri;;|it 
iii'oiiM(l.  itinl 
:iiit'u  is  lialt' 
'v.  is    iM'r|icii- 

on  I  lie    Ivllit'c 

liiiiliir  to  till- 
taut  tli.otiiK- 
(Tiicndiculiir, 

Ig    tilt'    WnriU 

ill  )in(^  ill  l> 

III'  till!   VCI'ti- 

I'vpliiiii  tliiit 
II'  li'ft  is  Ills.. 
;tt'iiijiiii4  till' 
II'  lii>ri/iiiit:il 
'il ;  ami  ymi 
I  point,  or  at 

lit  ill)  on  the 

(/  offint  fines      ! 

\']  Woillil    111-       j 

n-,'1'1'.  j 

arioiiH  wiiys. 
(t   cnil.  draw      i 
a  liori/oiital 


1 


yillMUIIT  l.ist.s. 


n 


liti.-:  from  it-*  riirlil   .'nil.  drnw  a  vortinil  liin'  ilnwii- 

wiu-ds;   alsn.  IVoii.   aliovr.  draw  a  vi'rtiial   lim'   l..  jnin 

till- ri',dit  iiid  III'  till'  liiiri/i.iital  liiu'.      A'^'ain.  ili"i"  ;iii 

oiilii|iii'  Inif  ;  iind.  |ii'rin'iiili(iiliir  to  its 

icntri'.  draw  aiiotlirr  wliirli   «ill   maKi' 

two   ri^lit    aiiKl'''*  ""    ''"■    ''''^^    iiliiii|iii' 

liiii',  as  sliown  at  V.      I'iii>ils  ri'pi'at   on 

ilii'  r  slatr>. 

Acute  AdkIbh. 

Ami  ninilelesK  flnni  ii  riijlit  iniijlr  is  (in  iKldr  iiin//i\ 
l)rawii  n^lit  aiijilf,  and.  midway  1m- 
Iwi'cii  till'  two  liiii's,  (ira«  all  iililii|iii' 
liiii!  mi'ctiiigtlu'  lirst  two  in  the  inriirr. 
orvi'rti'x.oftli('iiii},'l''at(r.  Tliis(>l.lii;ui' 
liiii'  di villi's  till'  rii^'lit  an^lc,  and  inalii's 
two  sliarpir  fDrm-rs  of  it.  'I'licsi' 
sliurpcr  corners  iviv  callrd  ai'iiti'  anj,di's,  l.t'caiisc  tliry 
arc  sliarpt-r,  or  more  iiointcd,  than  a  riglit  alible. 

ObtuHs  AnKlea. 

.1/;  iiinjli'.  i/irnfrr  tlmu  n  rli//tf 
iiHi/lii  '.">■  iiilli'd  (III  iilitiisr  inn/fi: 

Tliirt  figure  at  II  shows  wliat  is 
mt'ant   by  "gn-ati-r  than  a  right 

angle." 

Draw  a  Imri/ontal    line  as 
ill    I  ;    tlii'ii   ail    oliliipii'    line, 
joining  tlic  horizinital  lim'  at      j 
its  I'l'iiti'i' :   and  tlii'ii   a  tliird 
lint',     prriiriidiciilar     tn     tin- 

>l'('Olld      iilM'.  'I'll''      ll!li"ll      "f        i 


the    1 


iiiiu'    ]iiit>    I'linu-    iii:f    ai'iiti'      j 


I 


88 


rh.MUlKllS'    MAM  AL 


aii^l<-  and  oim'  olitiisi!  iiii^'lr ;  tlic  t'oriiiii-  to  llio 
ri<»lit  lit'  tin-  iihliijtic  liiii',  the  Iivtlcr  to  llic  Icl'f.  Tlii' 
union  ol'  tlit-  two  ol)lji|ui'  linos  forms  two  rij^lit  im^jlcs. 
Tims  (Iniw  till'  (litVrrcnt  ungli's  lit  viirioiis  po.si- 
tions,  ami  r('i|uii'f  tlic  pupils  to  naino  t1ii>  uncles, 
until  tlicy  can  readily  rciogni/e  tlicin,  liowi-vcr 
tlii-y  nniy  he  drawn.  Also  rci|uirf  llic  pupils  to 
makf  the  dift'crcnt  anj^dcs,  hy  placing  two  «tii'k.H 
in  dilfcriMit  positions.  Kxplain  (^Icarly  that  an 
iinj^lc  is  tin-  iliffi'i'i'iii'i'.  in  tlircrtimi  of  two  liih's,  and 
not  tlie  lines  tlicnist'lvi'S,  nor  the  spacn  botwccMi  tlicin. 
An  anj;!i'  is  fornifd  when  two  lines  tend  towards  each 
other,  thouf^h  they  do  not  extend  far  enou;,'h  to  meet. 
Good  drawing  niodtds  are  the  Itesiohjects  with  wliiidi 
to  illustrate  the  principles  of  giHiinetrieal  drawing. 

The  following  letters  drawn 
with  single  lines  illustrate  the 
dilVerent  angles.  Tietlers  K.  I"*, 
II,  L,  contain  right  angles. 
Letters  M,N,  V.  \V,  Z,  eontain 
acute  angles,  Ijctters  A.  K, 
X,  Y,  contain  acute  and  ohtusti 
angles. 


rr  i-v  ^M 


•  lOMniNINfi   SllJAKJlIT   LINKS. 


■TItlANMJI.KH. 


A  trianrfle  is  afir/iirr  liavimj  thri>r  stniif/lit  siitrs, 
enclosiiiff  f/iri'r  aii;//rs.  J 

A  BiKbt-anKled  Trianxle.  i 

A  ri'jht-diiffliul    /ri<iii(/fr  hus  our  <;/'  Its  (nii//rs   a      , 

riijlif  iiiujh'  (J  I. 

Draw  a  right  angle,  liy  joining  the  end  of  a  ver- 


U' 


m^ 


iiiir   to   lli(> 

r  left.  Til.' 
•ijjiil  unifies. 
iri<»us    |)08i- 

III,  liowcvcr 
0    pupils    III 

two  .stii'ks 
y  tliiit  iiii 
<i  liiit'H,  iiiiil 
t\V»'(!II  tluMii. 
owiinls  ciicli 
i;,'Ii  to  iiK'i't. 
■i  with  wii it'll 

ilriiwiii^;. 
'tters  ilriiwii 
IliiMtniti'  tlio 
-ctt.TS  \].  V, 
^]\\  iiii>;lt',«i. 
\',  Z,  coiitiiiii 
tti'is  A.  K. 
I*  iiiid  <)1)tiis(t 


ANfll.KS. 

alijlit  siiii's. 


fS    (Ulf//vS     It 

1(1  ot"  u  vcr- 


Sill.MUIir  USKS. 


'_".> 


ticiil   liii-'  to  til.'  imkI  of  u  liori/ontiil  line.      Dniw  mi 

ol.lic|l|c  lilM',  joillih},'   till-   otIliT   ciul.-.   of 

tlif  lines.     'I'lu-'so  tlim-  lines  will  jjive  ii 

tliree-,-iile«l    lij,'iiri-,   as   iit   .1,  wliicli    is 

CUlleil  a  triiUi:j;le,    lie.-illise    it    Illls    tlli-ii' 

aiij,'les:  iinil  a  ri','lit-:iii;,'letl  trian},'lc.  l.e- 

eaiisc  one  of  the  aii^leH  is  a  ii>,'lit  an;,'le. 

Here  is  a  eiirious  fact   ahoiit    tiiaiit^h's;   The  three 

im!,'les  are  always  .•-iiial  to  two  liglit  aiit,'les.  If 
one  is  a  right  angle,  as  in  the  present  instanee.  then 
the  other  two  will  he  etpial  to  a  right  angle.  Th'.s 
may  he  easily  illustrated  with  paj.e.  Cut  paper 
into  triangles  of  various  sha[ies  ;  then  eut  oil"  the 
corners  of  any  one  of  the  triangles,  ami  lay  them 
si.le  by  side,  .so  that  the  points  will  he  elose  together, 
when  they  will  be  foiin.l  exactly  to  till  tlie  space 
of  two  right  angles.  Mark  the  eorner.s  before  they 
are  eut  off;  otherwise,  the  right  corner.H  may  not  be 
laiil  together. 

An   Equilateral  Trlanglo. 

.1//    v.qidlaterol  trinm/h  /his  t/nrr 
i-'iiial  sI<Im  and  f/iirr  f/inil  inn/Irs  (K). 

It  will  require  coii.siderable  practice 
to  draw  an  ecjuilateral  triangle  cor- 
rectly. For  tlie  present,  it  will  be 
sufficient  if  the  pupils  get  the  idea. 
They  should  name  tht^  lines  forming  the  triatigles, 
alio  the  kinds  of  angles  formed  by  the  lines.  A  tri- 
angle is  the  strongest  of  all  figures.  The  position 
of  three  sticks  thus  united  cannot  be  changed  with- 
out breaking  one  of  the  sticks. 


80 


rh:.icm-:i/s'  m.imm. 

An  Iinsoeles  TriAngle. 


1 


All    TsDsrr'fH    friiiii'i!i'    Inis    tiro    onhj   of  it.<   s!(ffn 
ClflKtl    (I->. 

Draw  a  )it>ri/.()ntd  liiu>,  ami  mark  it** 
rcntri'.  Fnnii  tlii.-t  rciiirc  ilraw  a  vit- 
tiiiil  line  u|)\vanlH.  .Fuin  tlif  ciid  of 
till'  virtical  line  Id  tin-  t-nds  of  lliu 
Iiori/Diital  lint'  l)y  two  ohli<|U«^  linen,  (W 
ill  \i.  ICrasc  tlic  vertical  lim-,  wlicii  an 
isosceles  triaii^jle  will  remain,  'i'lie 
j^  wonl    isosceles    means    liaving    equal 

loRS,  as  this  triangle  has  two  equal  si.les.  An  equi- 
lateral trianjjle  is  an  isosceles  trianj^le;  hut  all  isos- 
celes triangles  are  not  ecjuilateral. 

A  Boalene  Triangle. 

A  srnfpur  f)'!a>if/li'  fins  no  tiro 
of  its  siilrs  fjiiii/. 

Draw  three  strainht  linos  of 

unequal  lenj,'tli,    uniting'    their 

ends,  as  at  M.     The  word  sca- 

M.  leno     moans     limping-      This 

triangle  can  be  placed  on  no  one  of  its  sides  without 

leaning  to  the  right  (U-  left. 

rOMIlININf!    STKAKiHT    MNES, UECTANWJULAU 

KKiUUE.S. 

Aiii/ f>/iirr   Ii'iriii;/  four  strtth/Jit  sidrs  and  four 
riijht  innilrs  is  rolird  a  rertaiDj/r. 
A  Square. 

,(  s'/ii'irr  is  <i  fijitre  hariiKj  four  ct/iial  sides  and 
four  riylit  any  I  vs. 


1 


of  Its  sii/r.'i 
iiid  iiitirii  itH 

,  ilniW  II  MT- 

tllC     ('11(1    of 

Cllds     III'     llu! 

quo  liiK'F*.  iis 
itir,  wlicn  an 
Miiiiin.  I'll)- 
living  ciiniil 
H.  An  t'<|ni- 
Imt  ill!  JHDs- 


li'  htlH  110  two 

inlit  linos  iif 
initin^  tln'ir 
In'  woi'il  scii- 
])in^j.  Tliis 
sidi'H  witlniiit 


•AN<ilTLAIt 


?«?s  awrf  fouv 


al  aides  and 


ariiAianT  uyxfi. 


31 


I>!aw  II  ri;,'lit  ivn'^If  Kpciiing  to  tlio  r'\\i\\t,  wiMi 
till'  lioi'iiCDiital  ainl  vi'i'tii'al  lincH  nf  tin' 
HaiiH'  li'ii^lli.  I''i'<ini  tlii-  ii|)|ii'r  mil  of 
tlio  viTtifiil  lim-  ilniw  towanls  tin' 
rij^lit  II  liorizmital  liiii'  of  tin-  Mimic 
Icnutli  iiH  (lif  <iiii'  IpcIkw.  N'l'St,  iliau 
II  vi'Hical    linr    l■^nn^•l•till^;    tlic    iij,'lit  ^• 

fiids  of  tlic  two  liori/ontal  liiit't.      Tlius  \vc   liuvi'   ii 
hi|nari'  (Xj. 

Let  till'  iMipiU  fn'(|U('ntly  iiiinn'  tin-  lines,  ntati'  it' 
any  iiri'  imriilli'l,  iiinl  iilxo  ^ivc  tin-  iiuinlxi'  and  Kind 
ot'iin^di's  tlic  si|uai )ntaiiis. 

Tlic  piipil  liaviiifj;  Icanicil  to  draw  a  .-i|iiari'.  it  \\ill 
now  lie  well  tor  liiiii  to  work  within  ono  of  dcliiiito 
size.  / 

DlAMKTEUH  OK  A  Si^AUR. —  •/  iliniiirfrr  of  it. 
S'/aai'o  dli'idfs  tlii'  si/udrn  and  ifs  iifi/iosifi'  sidi's  Info 
tiro  I'l/idif  jiiii'ts. 

Draw  a  sciuarc  as  before.  Divide  oacli 
of  its  Hides  into  two  eiinal  parts  ;  connoct 
the  points  of  division  hy  a  vertiral  and  a 
liorizontal  line,  as  in  O.  Tiiese  lines 
give  tho  diameters  of  the  S'piare,  and. 
at  the  Haine  time,  divide  it  into  four 
equal  smaller  sipiares. 

Let  the  pu[)il  iianu!  the  kind  and  number  of  angled 
in  these  four  sijuares. 

Diagonals  of  a  Siii'AUE.  —  Lhirs  rotnirrtln;/  tin', 
opimsitn  ntii/h's  of  a  H'ltiare  are  ail  led  the  diuijonnl.t 
of  the  square. 


O. 


32 


IKACIIKHS'  MASVAL. 


lliiviiiK  tirmvii  ii  Hinmrt'  U'*  luturi',  ilriiw  <>lilii|ui' 
lilies  coiiiutHiih  the  oppoHiti'  lUiKlt'H,  Hit 
in  v. 

A<l(l  tli«  (liumtttcrH,  uml  r.<iuirt'  tlii> 
|iii|iilK  to  ti'll  liow  iiiuriy  mi^,'lt"*  uimI  tri- 
imnltM  IIP'  now  coiitiiiiuMl  in  llio  H<|iiiiri'. 
ami  t"  nivc  tin'  iiuiiic  of  fiuli. 
IfiiviiiK'li'iiwn  II  Ktiiiiiri' iw  li"for«',  tlividf  ifn  lioii- 
zontiil    Mif!:'H    into    tlin-t'    i-qnul    imrt!*. 
mill  tlifn  ilriiw  vcrtinil  liiii's  ronni'itiiiK 
iln>  piiint'^  of  division  as  in  Q.     Ni'Xt, 
ilivi.lr  tin- verticiil  sitlcB  of  tlio  Hqimro 
into  tlirt'd  oqiiiil  purtf,  and   tlien   draw 
**•  liorizontal  linen  ecnnectinK'  tlie  points 

„f  division.  Tlio  sijuaro  will  tiuis  bu  dividml  into 
iiimt  Binaller  miuarcH.  It  will  now  bo  woll  for  tlie 
pupils  to  divide  the  sipiare  by  a  larger  miinber  of 
vertical,  li..ri/.ontal.  and  oblique  lines.  TIk-  obli.pu, 
liii.-«  should  be  drawn  parallel  with  the  dianc.als, 
whilo  Mi«^  other  lini's  will  bo  paralU'l  witl'  t(<'.'  shloH 
.<f  the  scpiare. 

A  Square  oon»truoted  on  its  DlwnetaM. 

Draw  two  lines  of  eijnal  length,  one  borizont. 
the    other    vertical,    and    crossing    at    tiieir   centres. 
Through  tbo  ends  of  thoso  lines,  draw  other  lines  of  tho 
same  length,  horizontal  and  vortical,  with   their  ends 
uniting :  the  result  will  bo  a  square,  as  in  O. 

Tupils  shoiilil  bu  required  to  construct  squares  in 
the  manner  first  indicatod,  and  also  on  their  diameters, 
until  they  are  familiar  with  both  methods. 


1 


III  i'i'<|iiiri'  t)ii> 
Illicit"*  mill  tri- 
III  till'  K<|iiiiri'. 

finll. 

iviil<'  itrt  lioi'i- 

•  i><|iiiil  (lurtH, 
Ill's  ('l)nlll'<'till^ 

*  ill  Q.     Next, 

of    tllP    «<]Ulll't> 

iiiil  tiu'ii  ilniw 
\i\\i  tlie  points 
I!  tlivitU'il  into 
10  wpII  for  till' 
•gor  mimlMT  of 
.  Till'  oi>liiH'.o 
tb<>  *liiig(>'.»lit, 
wit''  ti".'  Hi<li'!* 


•meUira. 

'  hori/.unt. 

tiieir  <'i'ntr('s. 
itlicr  linos  of  tlio 
witli  tlii'ir  i'IkIs 
,H  in  (). 

,rui;t  H*]iisires  in 
tltt'ir  (liiimrtt>r!<, 
lodd. 


r 


HTItMUin    I.ISKS. 


IVi 


▲  IquW*  oonMruoUd  on  tU  SUgdlltU. 
Draw  two  lincN  of  ('(|Uikl  Irti^lli,  one  horir.ontul, 
tile  otlit-r  vertical,  ami  itohhIii);  at  tlnir 
ctntrcM.  Draw  otiit'r  lin«>M  coiuu'ctinK 
tlii>  i'liiiM  of  till*  iirnt  two  liiii'M,  ami 
tlif  rt'Hult  will  Ik'  a  »<(|iiurc,  U.M  in  it.  It 
will  III-  well  for  the  pnpilH  to  prartirti- 
drawing;  M]uaro)«  in  clilV)>n>nt  ponitioiiH. 

An  Oblong. 

An  ofihtiff  h'lH  four  riijlit  itnf/li:i,  but  imhj  its 
o/t/ttinite  sidfs  lire  of  I'l/tial 
I  c  mi  til. 

Drawa  liori/oiitui  line;  from 
it."*  fi>(U,  draw  dowiiwanlH  two 
viTtica!  liiu'x,  of  ciiual  Icii^tli, 
^-  liiit  It'MH    t'liin   tilt'  I'  ri/.ontal 

linu  ;  foiinect  till!  lower  ctiil.s  of  till'  vcrtii'al  liner*  liy 
a  Hueond  horizontal  line,  and  tliu  re.>tiilt  will  lie  an  ol)- 
long,  as  ill  S.  Frei|nently  requiru  the  |iu|iil  to  point 
out  thu  difttironcu  bvtwucn  the  ohlong  and  the  H(iiiare, 

CoMUIMNO  8TUAI(iltT  LI^K^<.  —  OHLiguK   FunrKEH. 
A  Bhombui. 

A  RhomhuH  huH  four  equal 
»iden,  hilt  its  aiiyles  an-  not  riijht 
anijhs  (T). 

It  will  he  observed,  that  in  the 
preMcnt  inwtunce,  while  two  of  the  t. 

Hides  are  horizontal,  the  other  two  are  oblique.  Of 
course  the  rhombus,  like  all  other  geometrical  fig- 
uru8,  may  be  drawn  in  any  position,  without  change 


\ 


M 


t^:.i<■ltKNs'  .t/.i.v(/,tA. 


of  t'|ii4riii-ti-i'.  It  io  ii'it  iM>i't.«i«ary  that  any  <'l  it^ 
ftiiii>f4  .ImmiIiI  lx>  liori/.iiiitiki,  ii4  it  im  not  iii-rrnKiiry 
ill, it  ,iii\  <>r  ilti'  MJil I'  tt  xi|mirf  xliniilil  Im>.     Tlif  |iii' 

piU  kIiomM  Im>  |Vi|l|i|i'i|  til  iiillllUol  till'  i'IioimImim  witli 
till-  Ki|nill'i',  UIhI  |Milht   mil     tllc    illtlilrliri'    lictWi'iM^  IIk' 

i\v<i  liKim'i*.  'riiif>  iIm'  xi|ii.iri'  liiiH  t'liiir  <'>|iiul  kjiIi-h, 
So  ItiiH  till'  i'Ii<iiiiImi4.  Till'  Ki|Uiki't'  liiiM  I'liiir  ri^lit  ikti^li"< ; 
Itiit  llii'  rliniiiliiio  liii-<  twii  iiciito  ami  Ivvn  olitiioi'iin^li'x. 
Ill  ili'liiiiii;^  ii  iIkiiiiIiiI''  III'  u  M|iiai'i',  it  in  iii'i'iii>i<urv, 
ilH'ri'l'iiii'.  to  ilt'M'iilii'  liotli  till'  >ii|ri  iiinl  lli<*  itii^li'M.  Ill- 
till'  ili'liiiilioii  wliiili  it«  iiiti-iiili'il  {'"I  till'  mil'  IIIU3'  In' 
laUi'ii  till'  till'  iitln  r. 

All  li){iin>)«  liivviii({  tour  htnii^lit  hIiIi'i*  an'  rallril 
i|iia<liilati'ral,  a  tiTiii  tliat  cinlirai'i'M  niiu  li  iiinri'  than 
I'l'i'liiiii^iilar. 

My  riiiinniriiiK  111"!  fiiitraHtiiiK  ilitU'n'iit  Ki'imii'tri- 
lal  tlu'iiri's  tht>  |tii|iilM  will  learn  an  readily  to  iliittiii- 
ynifh  ami  ih'scriln'  three  nr  I'liiir,  iih  they  will  learn 
one  iiloiie.  'I'liirt  involves  a  valiial)li'  |iriiii'i|ili'  in 
teaehillK. 

The  ]iu|iils  having  ilrawii  a  rhninhiH,  let  them  iliviih< 
it   into  any  mi'  iher  of  limilar  lij,Miri"<.  ii-i  they  iliviih  il 

the  sr|uan'. 

A  Rhomboid. 

A    llhonihniit   fiiT.i  j'oiif 

sldv.s  ;    wtlir   oj'  its   tnii/ffS 

mr.  ri'j/if  ttntf/in,  miil  oii/if 

till'     nnjiiisifr     sliirs      ni'i' 

fi/iiiif  (V). 

^"  The    termination  <>-/W 

nioaiiM  like;    heme   rhomhoiil   meaiiH  like,  or  re»eni- 

hliii),',  a  ihomhiis,     Kei|iiiie  the  |iii|>ils  to  'ontraHt  tho 


yrU.MUlll    I.ISHH, 


.'lA 


iiiiy  I'l  itrt 
,  iiiM-fitKary 
.    Til-  |>ii. 

i|||l>ll«  will) 
rlVVt'iu  till' 
■>|llul  xilli'M. 
^Iit  \\\\)i\v*  ; 
tiiMMinnli-. 
«  lit'rt'>.i«m'v, 
I)'  nii>{lt>H,  rtr 

Hill'    IIIU}'     Im' 

iiri'     rikllril 
llUtl'i'    tlliUI 

I  K'""""'*'"'* 
y  III  ilistin- 
r'  will  li-iini 
ii'iiiri|il('    in 

tlit'iii  iliviilii 

Ili'V  iliviilril 


I  hiiH  font 

.1,  (/;/(/  iiii/i/ 
uli/r.i      II  iw 

lilt  ion  o-i-i/ 
■,  iir  ri'Hi'in- 
•ontruHt  till' 


rhoiiil I  Willi  till-  rli'iniliU".  iil-i>  wiili  ilu'  i-IiImhh.  uh'I     j 

|Miiiil  out  llii>  ri'»fiHl)liiiM'>-K  iukI  iIm-  ilitVi-r«>in'i'<  iMiiiniu 
llif  tlii-i'i'  llunt')'".  TIm'  |iM|iil^.  Iiiiviiii:  ili-itwii  II  iliMiii- 
liiiiil.  oliuiilil  III'  ri'i|iiirii|  !••  i|i\i'li'  it  iiil>*  miv  iimihIm  i 
III  -Miiil.ir  li;.'iiii  V  It  will  !'••  wi'll  »••  <l'i  llii«  rf|H'iil- 
••illy,  TIk'  rliiiiiilHiiil  ;iii'l  till' iilili'iiu  ai'i>  ImiIIi  laljiil 
|iiinilli'l'",'niiii''.  Iii'iuii»i'  ilii'.v  liiiV"'  lliiir  M|i|i'i-iii'  »ii|i'« 
i'i|iiiil  iiml  jiaiiilli  t. 

Till'  ti  iiilii'rwiiii  U  Hiixiiiii'-  ti.  iiii|iri'i»«  iiii  iIh'  mhii'I- 

nl    till'    |ill|iil«    ll"    llfllll.V  II-  liiCKililf  till'  ililVi'Ti'llt  li'lIM". 

Ill  |iliiiii'   Ki'uiiiitiiiiil  lluMii'x.  mill   l-i  liivi'  inlililioiiut 

viii'ivt.v  I"  llif   in-tinrii «ill   lln'l  u  '"i"'!'  «iili  it'« 

Iwit  I'luU  tml  lii>{itlii  r,  I.I'  xt'rvii'i-,  wln-n  ii.»iil  ifi  tin- 
|nllii\vin«  iiiiiiiiii'i  :  l.i't  ilii'i'i' piipiU  tali.'  Inlil  nl'  tli. 
n.nl.  1  iuh  Willi  'iiu'  limiil.  iiinl  iImh.  at  ii'i|iU'-t<il  I'.v 
llii'  icailifr  "f  any  nni-  uf  ilu-  vUxnn,  Wt  tlii'in  »">  Im'I'I 
till'  I'linl  111  III  I'lnn  a  riwlif-aii^iliil  triaiiuli-.  an  i'<|iii- 

lali'i-al  Iriiiiiijif. 'If  aiiy<itlMr  Iriant'Ii'.  an  llii'  Main • 

i^ciM  I'li'K.  NrNi,  III  r"iir  |>ii|iil»  talii'  liiiM  ol'  tlu'  ronl. 
uiiil.  in  u  Hiniilar  iiiaiiinr.  I"i'ni  ililViiiiit  l>iiir-»iiliil 
li'^iircK.  Fivi'  iiupili  niiil.l  fiiiin  till'  iM'iitapiii,  xis  pii- 
],\U  till-  lii'xa^'i'ii.  ami  ^.l  mi.  All  tln'  ll;;uii'»  Inniii'il 
iiv  till'  Hjinii'  I'linl  WHiilil  liavi'  tlii>  hiiiiii-  liiKlain'c  ai-ininil 
tlii'iii,  iiiid  Hii  wunltl  Ih-  iHiiiM'iiini'lriral. 

Till'  jiriMi'ilin^;  I'ViniiiM  slmiilil  ln'  fairly  nmlri- 
hIiiihI  Ity  till'  impil'  lu'l'iri'  tln'V  ailvaiui'  lartliir.  It 
In  not  lUH'c'HMiry  tliut  tliry  i*ln>ulil  Im'  uMi'  to  draw  ilir 
liKiircM  uccumti'ly  ;  lait  tin  y  sIiouM  In-  abli'  Ici  ;;iM' 
tlii'ir  naIlll'^<,  anil  tii  ili'sn-ilii'  tlicni  with  n'ailiiii'H>*. 
TiarliiTK  ran  iiirna"!'  tin-  lovi' iil'llu'ir  inijiilM  I'm'  lliiir 
work  by  ilrawinn  for  llu'iii  tlif  ninipli'  oiitliin's  of 
oltji'i'tn  wiiiili  riiiiii'  iiiiiliT  tlirinlaily  uliMiviitinii  in  tin' 


tltt 


nA'HHMf*'   MlSIAh 


...|,.H.|r.H,n,  ..r  ti.  ih.'  vlHnUy     Hi«m|'I-  r..ini..  •»• 

,H....l  m  .irulrfl.i  IMM-.  UI..I  .xlul.ihhn  III.-  «.'..m..irk' 
r.u.f.ir.-  ..r  til..  |.r.-.-...|iiii»  .■«..r.i..-.  will.H.nr  i.M.v..ry 
l,.ii.h..r.      •|'.-.Ml..r«  <li-.ul.l   r..n I»r.  ihui   ui    »lii* 

|„.,.r.l.  III.  V  -h'.iil'i  I oii»tr.MJ..|  Willi  .l..|liiit.'.»im|.l.« 

|,r..,H.rti..i,V     l»r,»wiM«  .liouM  ulwuy.  I"'  tmiuH  ..- "« 

,„. lin |m.|mU   im.i.i   I..'  tuuul.t   llr.t  t • 

,ti..|  uii.l.r-tuii.l  til-  i.r..|H.rli..»..  uimI  |.r..|M.rtM-  »t  r..rii.» 
«n.l  ..l»j-.'«..,  otlurwi...  tli.-y  .■•.i,  n.v.r  .Iraw  tli.ni 
i,,t..|li«.mlv;  uii.l  til.-  .nrli.T  .-x.-r.!!-.-. -.li.'iil.l. 'l'"'"- 
for..  I..'  »<  «»- 1>  Ik  .liiUiM  t.r  tliut  tl>.-yi»»  »-..in|.n'l»"h.l 


tl 


liMII, 


Kvi-ry  prinmry  H.ti.M.tr.>..m  «1i'Mi1.I  Ih-  Hii|.|.li.a  witli 
n  J.t  .if  i-iiiiiurv  mIi'h.I  h.'mU.U  'n..-  I'l"'!'!*  ""' 
v..ry  nm-lnl  f..r  lixinK  i"  «•'"  "'''"'-  "»"  >'"""«  I*"!"'* 
II  liii.ittl-'l«"  •••'  «'">ii>''»<''''  l'"''"^- 

Tl.i.  iMM.k  in  HiM-iully  .UiKii.Ml  f.-r  lli-  " t  i.-m-H. 

vTH   la  nhow  tli.Mii  how  tu  .■s..fiito  tliM  .ImwiiiK".  uihI 
lu.i  t..  iii-trii.t otl.oM.     Tli.y  ur..  ...xiHM'ti.l  t..  ..x|.luiii 

..vry  tliin«  in  liUiKuiiK"  "•v"  "'"f"  I'ii""!"^'-  "'='"  ''"'♦ 
„f  tl'f  l...nL  tluit  y..»i.K  .liiMn'M    may  !..■  al.l-  .l.Mily 
t..  .....l.-r^taiMl  tl...  tl.ii.KH  tuuKl.t.     TJii-y  hIu.uI.I  not, 

liowm-r.  lull  into  tli..  .-rrorof  i*ii|.iH.sin«tliut  rlMl-livn, 
,.v.-ii  M"it.-  V.M.i.K  rl.il.lnii.  .•ui.i...t  1'.'  r.u.l.ly  '"'"I"  '" 
,M.,l.-r«tiii..l'  tlu'  i.u-ui.itiK  of  l.'"i«  «-..r.ls  ..r  -n.-i.till.' 
wnnU.  Inruu..-  tli.-y  iiri.  long  or  Hoifntill. .  WlwiH-vr 
tl„.  m.-.u.iu«  of  Mi.li  wor.ls,  loroxiUiipl.MiH  ixtihmhIu- 
„1,^,,  ,..,uilat..nil.  rl.o.nlM.i.l,  \*  vi.il.jy  illiHtnit..!,  .iiil- 
.livi.  .an  iih.l.  THtun.l  tlu-  wonl '  li'*  f'ulily  uh  tlioy  can 
„„a.-rst.in.l  tl..-  nimininu  ..f  ri«lit,  l.-ft,  mpmn-.  iin.l  will 


i»rni«,  I'Mii- 
••  |{i'))iiii'lrlu 
■iir  liM'Vi'fjf 
iiki  iki  tlii« 
ivi'h  I'll  till' 
|iiitiM>ini|»li' 
imnlit  n»  'III 
iH  'I  iitfiifimj 
\\r*t  !•»  »«'•• 
tii'Mof  foriiiM 
ilriiw    tlii'in 

llllllll,    til''!"!- 

i-iiiit|>r«li<*tHl 

ii|i|iliti|  with 
'  luiHli'lit  iin* 

i'<)llllt<   ]MI|lillt 
IMt'llf  Iflicll* 

rawing'*,  iiii't 

I'll  to  i'\|ilskill 

iiir  tliuti  Hiikt 
i.  aJ.lc  rli'iuly 
y^  Hlioiiltl  not) 
lint  I'liilili'fii, 
ulily  iniiilt'  to 
t,  or  Hrifutilltt 
Wlu'iii'vcr 
iiM  j)t'r|H'iitlii'- 
iHtriitid,  (liil- 
ly  UM  tlii'y  can 
|iiart'.  iiiul  will 


hrttMuiii  ustn. 


a: 


tiikf  prt-l.'  Ill  «i-iiti«  <l"Mi.  H"tM..  i...i.'hi'r»  *\mM 
n,-v  lliui  |Mi|iil.  ur-  iiiu'l.'  .i..|imliir.-<l  with  llio  phwI 
tnrt'y  of  Jill'  «.mI.hIiuI  wor.l*  thtU  iimi»«  »»  rr..|>i.iiily 
ii..m|  ill  timliiiirf  .lr.k«i".U.  if  tl"'-'-  >*'"•  ♦'■'"''  ^""''' 
,.x,„..,.  tiM'i Iv<-  ••>..llv  uii'l .  U'trly.  imi-I  I»'»v..  tli.'lr 

|iii|til»  I'lirii  »•»  il"  il»*  *»»»''• 

|>.i|.i|.  -Iio.il.l  tjruw  rn..|u.nily  "ii  »!•••  Mn-  hi»"iir.l. 
k  tiling  tli.y  HI"  ul«iiy»<l"li«l'""l  «"  '!"•  Wli'Hi'f 
ll,.'y  .Iruw  ..u   til.'    l.lu.  kl.our.l   or  ..n  tli"  »lnti',  tli.-y 

kIio'iiI.I  iH.t  111  rtr:.t  «!••••"' """■'"'"'"  '"  ""  '"''"'*  '" 
niiilii.  tlnir  liiM*  l..u.tiir.il.  'n.-y  »\m\l\  rutli.T  l.'.irii 
to  .Imw  Willi  l.oMii.-.»  uh.l  ia|.i.lity.  .-vMi  Iroiii  tl..- 
,Mit..t :  mriir.My  of  tlhioli  will  .oi.i..  from  prmti.... 

Il  liuM  Im'..||  Im'I'I  l>y  iii'ii'v  'I"''  '••«il'l>'''  ""•'  "" 
olli.r-.  wImm.  tlu.y  iM-uiii  U>  .Iruw.  «lioiil.l  l-niii  wiili 
huliiiul  ol.j.M  t*.  mi.l  not  with  »..v.'rn  «.'oiii.'tri.Mil  foriii*. 
Hut  i'urMfiil  I'xnmimiti'iii  of  r.'-iilt-  in  Kiiropr,  .lunii« 
tli.<  li».t  twi'Mtv  yur-.  hIiow*  timt  tli-  fninuT  in  not  tli- 
|«.,t  wuy  to  lM.«"in,  tl.ou«li  it  iii.»y  I."  lit"  l""t  w;iy  to 
..n.l ;  uii.l  .•.iH..ially  it  i«  not  tin.  lM.».t  wiiy  to  Im^hiii 
wlii'ii  till'  iiim  i-*  to  i.ro<lu.'..  in«lMHtriiil  ivniilt^.      Draw- 

inn  •>■'•"'  •"•""•"  '""'  •'"'"  ''"'  '"""""  ""'"""  "'"'"''  '"" 
iniiinly.  in  iv  romiilMvl.oiit  un.l   lalioi-ioin  way  to  mi-Ii 

ri'Kiilt-*.     Of  ••<»iirm«  ii  liiiiitiul  iiiiioiint  of  .liiiwin«  fi < 

n.Umv,  for  tl..-  -ak.-  of  vuri.'ty,  i-  not  only  tu  1...  p..-     - 

„„ii...l,  l.nt    .•n.o.imK.Ml.  at   all    tiin.H.*    Tl...    im.,.iI-|     I 

,1, ..v.'ii  lit  tlu.  outsi't,  .houl.l   li.'    ina.lr  acinaint.-.l 

with  tl.  ..in.'tri.iil  foriiin  ami  t.Tin^  tlmt  th.y  nmy  i.ft.r- 

wunU  Ik-  iil.l.'.  nn.l.r>itan.lin>.'ly,  to  .l.K.rilir  aii<l  .liasv 

ol.j.TtH  <.f  all   kIn.lH;  tor  ol.j.'.tH,  wIihImt  natural  or     | 

arlili.ial.  im-  usually  hiw<"l   on    n-wnlar    P'oui.'tri.ul 

foriim.      Without   a   UmowIu.Ik'I'  of  tln-^f   ponntri.al      1 


88 


TKA('llh:i!.'>'    UAMAL 


foniH  till"  iirtisim.  in  piirticiiliir,  riin  liavo  no  rli-iir 
a]>|)i'i'iiat inn  nl   liis  wurk. 

A^'iiin,  it  is  ciiMtniry  Imtli  in  I'Xpcrit'iici'  ami  \><  tlif 
|irinci|il(.'s  i)t'  ;,'(>imI  ti'acliiiij?  to  .sU[>iiosr  tliat  pupils 
fan  ilraw.  with  any  flcjjrcc  of  accuracy,  a  coiu- 
poMhil  cnivc,  like  tlic  o^cc,  or  tin'  dclicatdy- 
wiivini,'  lines  wliicli  arc  seen  in  the  I'oruis  of  niitural 
ulijcts,  wlicii  tlicy  arc  nnaMc  to  draw  a  ,strait,'lit 
line;  or  to  suppose  tliey  can  draw,  with  any  de- 
gree of  accura(!y,  such  irregular  forms  as  those  of 
iiniunils  and  trees,  whose  proportions  can  only  he 
f,'U((ssed,  when  they  cannot  draw  regular,  syniuietrical 
forms,  whoso  exact  proportions  aro  known;  or  that 
they  can  draw  ohjccts  from  nature,  involving  tin'  dif- 
iiculties  of  shade  antl  perspective,  wluui  they  cannot 
drau  from  Hat  copies,  without  shade  or  perspective, 
those  symmetrical  forms  whi(di  always  Inive  bccMi,  and 
still  are,  so  extensively  employed  in  practical  design. 

IIcucu  it  is  that  this  course  of  drawing  begins  with 
geometrical  forms  illustrated  hy  models;  gives  pre- 
cedence to  that  which  has  delinite  proportions,  and  so 
permits  the  drawings  to  ho  veritied  hy  actual  meas- 
urement;  puts  tho  symmetrical  before  the  unsym- 
metrical;  and  works  with  Hat  copies,  making  tln^ 
pupils  familiar  with  pure  form,  and  teaching  the 
principles  of  practical  design,  before  taking  natural 
objects,  which  involve  perspective,  light,  and  shadow. 


Qui-.srioNS.  —  WImt  is  a  point  >.  Dt'scrilH"  tl>«  ditTcrcnt  kinds 
of  straij;lit  lines.  WImt  is  the  ditrorcncc  hctwccn  a  viTticiil  and 
11  iicrpfiidicular  line  f     WImt  two  tlnn;,'s  aro  rcnuisitc  to  nmku 


VO     111)    I'Iriir 

•  and  til  till- 
tlial  pupils 
K-y,  11  ciiiii- 
(Icliciitcly- 
s  III'  iii'tiiriil 
{  u  fitniij^lit 
itli  liny  di'- 
as  those  of 
■an  only  Ih- 
synmu'trical 
\vn  ;  or  tliat 
vin}^  tilt'  dit- 
they  cuuiiot 
perspective, 
ive  been,  and 
tieal  design. 
;  begins  with 
i ;  gives  piv- 
'tion.s,  and  so 
actual  ineas- 
the  uiisyni- 
making  the 
;eaeliiiig  the 
king  natural 
and  shadow. 


!  (JitTcront  kind.') 
II  a  vcrtii'iil  iind 
i|uisitc  to  iimku 


.S77M /'.///'  /./AA.'.S. 


yu 


liiK'^  imnilli'l  '.  Wliiil  is  -aid  <ii  dnivNiii;;  lim-  in  dill.ivin  iliivr- 
tiiiiiM  ;  or  ilitllri'iit  IcnKliis  >  How  would  voii  divi.lf  n  liiir  iiii<> 
sis  .■.imil  purls  '  Into  M'vcn  >  Wlmt  i.s  iiii  iinnie  <■  Di'MTJk'  tin- 
.lillriviil  klmls  of  iiii-k's?  WIml  is  ii  liiaii«lo  ?  UcMMil).'  lliu 
dill'cmit  kiihU  of  liiiiii;;ii's  '.  Uliat  is  llif  dimTiiire  ImIwccii  an 
isosiuli's  tiiaii«le  mid  an  iM|iiilai.Tai  tiiiin-lr  '  Bciwiuii  a  .iiiad- 
rilateral  and  a  rcctan},'le  >.  Hctwirn  ii  squar.;  an.l  a  riiomliiis  ' 
Bilwi'cn  an  oldon;;  and  n  rlioinlioid  '  What  is  tin:  diainetcr  uf  a 
siinaro  >.  lis  dia;;onal  >  How  sliould  diawiii^;  always  \\r  taii^lit  ' 
What  is  said  of  ^ivint:  .  Inldrni  Ujii-  UMhr.ical  words?  Mow 
doi's  this  course  of  diiiwiub'  Iji'giu  '■     Why  dots  it  so  hcaiii  '. 


CHAITKll   11. 


STUAlCIIT-hINK  FKil'KKS. 

TiiK  pupils,  hiivin^?  Ix-fDim'  f'aniiliiir  witli  tlu'  prrccd- 
iii<^  cxcrfiscs,  sliDiilil  lii'^jiu  to  (Iniw  iVoin  furds,  tiinlcr 
til.'  ilircitidii  of  the  tcairlicr.  Tims  lar  tlicy  liavo  l>ffn 
t;iii!,'Iit  rnlurtioii,  since  tlu-y  were  rcipiircd  to  iiiiiko 
tlicir  (Irawiiijjs  sinallcr  tlian  flw  ti'aclii'i's  Maiklioanl 
copies.  Tlie  canl  exen'ises  will  teach  tliein  iiilnnjc- 
iiii'iif,  since  tliey  slioiiM  lie  leipiircil  to  make  tlieir 
ilnvwin^js  much  hir«er  than  the  card  copies.  These 
two  modes  of  practice,  />i/  rii/iiiti"ii  <uiil  fii/  riilonje- 
iiinit.  should  j,'o  hanil  in  hand.  Hoth  are  essential  to 
(^ood  progress. 

<'AUI>-K.VKK<:ISK    1. 
Vertioal,  Horizontal,  Oblique,  and  Parallel  Lines. 

Draw  verti?;al  lines  the 
whole  h'ngth  ot'  the  .slate ; 
then,  heginning  at  one  end,  di- 
vide them  into  (Hjual  parts,  first 
of  indefinite  length,  next  of 
definite  length,  as  one  inch,  an 
inch  and  a  half,  &c.  Draw 
horizontal  and  ohliijue  lines, 
ilividing  them  in  a  similar 
manner.  Afterwards  draw 
vertical,  horizontal,  and  ohliciue  lines,  and  divide  them 


^ 


,s n/A in II I- 1. 1 .V i:  >'/'v uhkn. 


4t 


li  tliu  jirrciMl- 
curils,  \inilcr 
I'V  liavo  lii'tu 
iri'd  to  iiiiilvn 
s  liliu'kliouril 
licm  riiliinjr- 
I  luiiUc  tlii'ir 
)l)ii's.  Tlu'so 
/  I  III  ndoriju- 
V  t'sscntiiil  to 


tllel  liineB. 

lines  tlu> 
f  tlu'  slate ; 
t  one  cntl,  <li- 
luil  parts,  first 
gtli,  next  "f 
s  one  inch, an 
f,  &c.  Draw 
i)1)li(jue  lines, 
in  a  similar 
•wards  ilr;iw 
d  divide  them 


I 


into  a  K'Vfii  numlH  r-.r.'.iiial  [.arts,  as  two,  three,  four, 
MX,   eight,    ten.      To   oi.tain    lour  e.pial    j-arts   lirst 

divide  the  line   into  tw jind  parts,  and  then  divide 

eaeh  of  these  parts  into  two  eipial  parts.  To  ol.taiii 
hix  e(p,al  parts,  first  divide  the  line  inti>  two  e.pial 
parts,  and  then  eaeh  part  into  I  line  e.pial  parts. 

Frequently.  i)elore  the  i)ni)ils  l.e^'in  to  draw  IVoni  a 
eard,  the  teaehi-r  shotdd  re.piirr  them,  as   a  .  la^s  and 
under  his  direction,  to  analyze   the   copy,  and  ^'et  a 
clear  understanding  of  its  features.     Thus  t<.  analyze 
each  copy  would  consuin-  too  much   time,  nor  is  such 
an   analysis  of  each  copy  essi'ntial    to  a  dear  nnder- 
htanding  of  the  exereise.s,  as  each   feature  is  usually 
„ften    repeated   in   the  dift'ereut   exercises;    hut    the 
preliminary  analysis   should   r.-ceive    cpiite    fre.pnnt 
attention.     Many  elahorate  .Irawings  heeome  easy  of 
execution  the  moment  analysis  has  n.ade  Ui.own  their 
elementary   lines   or  forms.       .Vgain.   tiiis  analyzing 
process  shows  how  much  of  the  previous    instruction 
has  heeii  retained,  while  it  also  tends  to  develop  the 
perceptive  powers  of  the  pupils. 

CaKI>-KxEU<  ISK    II. 
Right-Line  Figures. 
Having  placed  a  canl  in  the  liamls  of  each  member 
of  the  class,  conduct  the  analyzing  exercises  after  tho 
following  manner :  — 

FOKM   (1. 

7Vvfc//cr.  — What  lines  in  this  figure? 
^„.s.„vT.  — Vertical,  horizontal,  and  ohliipie  lines. 
7V,„.//c»-.  —  Into  how   many  parts    is  tho  vertical 
line  divided '.' 


42 


lEMIIKHS'    MAS  UAL, 


h 


AitHii'ft'.  —  Four. 

'I'l'itr/ii-r.  —  H<i\v    \Miiil(l    yon    hi'j^iii    tn    dniw   tins 

,liisirrr.  —  First  ilriiw  tli<'  viTtii;il  line,  Hint  dividr  it 
into  two  i'(|iial  |tiirts.  'riii'oii^j;Ii 
till-  ])(>iiit  of  division,  draw  a 
lioi'i/oiital  line  ol'  tin-  f*iiuu' 
li'ji^tli  as  tlic  vi'i'lical  lini',  oni- 

lialf  to   till'   rinlil I'nK'  t" 

tin-  li'l't,  of  till'  vcifical  liiii'. 

yV,/. ./„,■.  —  What  is  tin- 
iianu'  of  tlic  tiij;iirc  drawn  on 
the  vertical  and  lioii/.nntai 
liin's  ? 

Aiisim:  —  A  Mpian-. 
Tioi'lnr. —  How  is  it  drawn'.' 
Aiimni'. — On  itH  diaK""iilf' 
Tiiiflin:  —  Wliat  is  tin-  diaj^onal  of  a  si|uarr'.' 
Aiixwi'i:  —  A  strai^lit  line  connect ini;  o|i|icpsiif  an- 
gles of  a  s(|inire,  ami  dividing  the  siinan-   into  two 
equal  rif^lit-aii^lcd  triangles. 

Ti'iii'liri:  —  How  many  diugornds  can  a  si|inii'o 
have '! 

Ausirn:  —  Two. 

Triir/iii: — When  drawn,  flow  do  tliey  divide  the 
w|uan>  ? 

Aiisiri)'.  —  Into  four  e(|iial  rif^ht-anf;led  tiian|,'les. 
Tiiif/,,r.  —  How  do  yon  olitain  the  ]ioints  for  this 
j     sqmire  V 

I         Aiisirrr.  —  I>y  dividing;  each   half  of  the   vertical 
f.    and  horizontal  lines  into  two  equal  parts. 

Triir/in:  —  How  do  you  then  coniplete  tliesi|uare  V 
Aiisirri:  —  l>y  drawing  obliqut!  lines  to  eonneet  the 
[joints  of  division. 

It  is  not  to  he  expecteil  that  young  children  will 
give  answers  correctly  as  here  set  down.  The  fore- 
going is  presented  only  as  a  suggestivi-  mode  of  con- 


<» 


4  » 


rt 


til      lll'ilW     lIlIM 

ic,  iiiiil  ili\  iili'  it 
irts.  'riii'iiiii^Ii 
vir4iiiii.  draw  ii 
III'  tlh-  tuinxr 
rticiil  liiii',  niic- 
lil,  iiiH'-lialt'  III 
dtiial  liiii'. 
Wliat  i.-^  till' 
;iirc  drawn  nii 
tiid     li(ii'i/.i>iital 

s(|niU't>. 

ow  is  it  drawn'.' 

a  t^i|uari' '.' 

Ij,'  ci|(|insitt'    aii- 

Hiiai'if    ill  I"  Iwn 
ciiii    a    si|iiai'u 


lioy  dividf  the     ' 

fK'd  tiiuMfilt's. 
]M lints   for  this 

of  I  lie    virtical 

•tH. 

('to  tlu'  Hiiuure  V 

I  ti>  ('(iniu'ft  tilt' 


i;^  <'Iiildron  will 
iwn.  'I'lu'  t'ore- 
•  miidi'  <it'  coll-     I 

I 


h 


y» 


\ 


4  ft 


ti 


STIlAUniT-USE   FUiVUt.s. 


.\:\ 


(liirtiMK  til.' analyzing  cx.Ti-is.-.      Adapt    th-    nuidi'  of 
luiiilysis  to  till-  nipai'ltit's  of  your  piiiiil.-*. 

It  will  1)1'  olHiTVi'd  tliat  till-  answ.-rs  aiv  alilnvvial.'.l 
in  till'  test.  Kxiii'iifiKM',  how.'ViT.  lias  slmwii  tliat  it 
is  wvll  riv(|iicntly  to  ri'(|uir.'  small  cliildivn.  wln'ii 
uiiMWi'rini,'  .lut'stions,  t«>  niiilio  ourli  aiiswi-r  a  comi.l.N' 
Htatcni.'iit.  Do  this  at  tini.'s  in  th.-  analysis  of  f.inii>: 
Thus :  — 

7;„,./,,.,.._  Wlifvt  is  tilt'  diiiK'oiiid  'if  a  s.iuaif.' 
/'„/,//. —Tho   tliaK'onal  of   a  s.piaiv   is   a  straij^iit 
lint'  fomifftiiif,'  t)i)iuisiti'  an^lfs  of   th,:   s.iuaiv,   ami 
tlividiiiK  if  into  two  ftiual  n«lit-aiiK'li'd  tnani;lfs. 
7V,„./,,,,  —How    niiiny    tliugonals    tan    a    s-iuarc 

havt'? 

l'„inl.  —  A  »<iuuro  <aii  havi^  two  ilia>,'""als. 

Mii.h  import aiiff  is  justly  attafli.-l  to  this  iiiodf 
of  aiiswfriii«,  fsiifcially  hy  small  .diihUvn.  It  is  not 
only  a  h.-ttfr  test  of  thfir  kmnvlftlj,'.',  hut  trains  them 
to  flt'ar  statfim-nt.  To  i-ractist-  it  constantly,  how- 
over,  wotdd  ht'fomt'  Wfarisonif.  and  would  foiisuiiif 
ttto  niiifh  tinu'. 

l.',„j;^,  /,. —  Draw  a  vertical  lim-.  tlivi.h.  it  into 
thinls;  throU!:!li  the  upi-fr  iioint  of  division,  draw  a 
liori/ontal  lint>  ftiual  to  twt)-tliirdst)f  thf  vfrtical  line  ; 
antl  tluMi  fomplftt*  thf  iinuro  hy  tlrawing  thf  ohlitiuf 

liiifs. 

KniiM  ,-.  —  Draw  a  square.  I'intl  tht*  mi.hlif  of  thf 
ujiptT  sidu,  untl,  l'rt>m  this  point,  thaw  a  Vfrtital  liif 
upwards,  (".lual  tt.  t.m-half  oftlif  k-ngth  t.f  tht;  sith-  of 
thf  stpiart'.  From  thf  uppt- r  futl  t)f  thf  vertical  liiif. 
draw  ohlitpit!  lines  tlt)wnwar.ls  to  the  Ifft  and  right, 
striking  the  uppfr  corners  of  thf  s-iuare.  and  projftt- 


■\ 


^4 


TKACIIKHS'  MASVAI.. 


\ 


.  ,  .^lijjlitly  lu'yoriil.  Draw  tlio  pncalli'l  nhlicjiit'  lines, 
.,<i  tinisli  lis  in  \\w  copy, 

FoHM  it.  —  i>riiw  II  Miiiiiiro  uiul  iN  diiiK'nivIx.  IIiilvc 
t'licii  M<'mi-<lianoiiul,  ami  tlirou^li  tlic  poiiits  of  diviH- 
itiii  ilraw  the  iiiin'i'  sipiart'.  Kiiihc  the  dottt'd  linnH. 
'I'licso  two  HqiiiiioH  ari'  calit'd  (lomt'iitric  sipiait's,  lic- 
causc  tlioy  liav»>  tlio  Humc  ccntro. 

Wiirii  tlic  pupils  lire  drawing  from  tlio  cards,  and 
after  tin-  first  liiif  to  lie  drawn  lias  lu'cn  sidcctcd,  statu 
liow  lonjj  tlio  line  is  to  bo  made  on  tlie  Hlntps.  Wlien 
they  have  drawn  the  lino  of  the  desijTiiated  leiif^tli, 
and  in  the  position  it  lias  on  the  .-ard,  then 
the  tciu'her  should  draw  it  on  the  hiaekhoard.  Thus 
proceed  with  each  line.  In  this  way  the  teacher's 
drawinj,'  will  eonlirm  the  work  of  the  class,  and  not 
serve  as  a  ropy.  In  this  way,  too,  the  meml>ers 
of  the  class  will  he  kept  together,  and  instructed 
as  one  pupil.  The  aim  should  ho  to  work  with  a 
good  degree  of  riipidity,  though  the  Hgures  may  not 
he  accurately  i'xecuted  at  first. 

At  this  stage  pupils  should  begin  to  draw  lioth  from 
memory  and  dictation.  That  is  memory  ilrawing, 
when  the  [uipils  ure  required  to  reproduce,  without 
definite  instructions,  forms  which  they  have  previously 
driiwii.  as  they  might,  in  this  ca.se,  he  required  to 
draw  frinn  memory  an  equilateral  triangle,  a  sipiare 
on  its  diamclcis  an  ohiong,  a  rhombus,  or  a  rhom- 
hoid.  The  teacher  would  simply  direct  the  drawing 
of  any  one  of  these  figures,  and  the  pupils  would 
execute  it  from  memory.  That  is  dictation  drawing, 
when  the  teacher  dictates,  but  does  not  draw,  the 
lines    for   the    composition    of    a    new    figure.      The 


V 


» 


il» 


*"> 


'1  nlili(im<  linoM, 

i({i  nals.  Iliilvt* 
[toiiits  of  (liviM- 

10  (lottl'tl    lillOH. 

ric  H(|tmu'H,  lic- 

tlio  <-uri]s,  mill 

11  sclt'ctt'd,  stivto 
■  ulates.  Wlu'M 
ignutfil  Icn^'tli, 
lie  .'iml,  tlli'll 
•khoiinl.  TliiiM 
y  the  tuiK^lii'r'H 

class,  iiud  not 
,  tlio  inenilnTs 
and  iiistnictiMl 
r»  work  with  a 
IguroH  may  imt 

draw  liotli  from 
•mory  drawiiifj, 
rndiK'o,  without 
liav*'  prtn'ioitaly 
bo  required  to 
angle,  a  siiuaro 
lus,  or  a  rhom- 
ict  tho  drawing 
0  pupils  would 
tation  drawing, 
not  draw,  tho 
V    lijruro.      The 


) 


V 


r* 


/"» 


i 


SlHAWin-USK  yiUVHKS 


4ft 


pupils   draw.    f..llowing   th.-    words   of    th-    t...uluT. 

TuU«'  tjgiuf  A,  for  <'xampl('. 

Tho  ti-afhcr  dictatt-s  lhu«,  whiK-  thf 

pupils  fx.c\iti' :   •' Draw  a  vcrtii-al  lint- 

fouf  inchi'M  in  length;    mark   its  v.vw- 

tre.  and    from   it,  to   the   right,  draw 

a  horizontal   line  two  imhes  in  length 

From  the  end  of  this  horizontal  line. 

draw  downwards    a  vertieal    lino   two 

inehoH  in  length.'' 

This    illustrateH    the    general    mode  ■*• 

of  conducting  dictation  exercises.     The  teacher  must 

be  very  particular  about  the  words  used. 

The  memory  exercises  show  whether  the  forms,  and 

the  modes  of  tlrawing  them,  have  been  clearly  and 

permanently  lixed  in   the  minds  of  the    [tupils.     Of 

course  the  memory  i-s  greatly  strengthened  thereby. 

The  dictation  exercises  show  the  perfect  interchange- 
ability  of  words  with  lines  ami  forms  :  thai  a  form 
'  can  be  drawn  from  words  us  well  as  from  a  <opy. 
They  also  strengthen  tlu;  imagination  ;  since  the 
pupils  are  compelled  to  make  a  mental  picture  of 
what  is  required  by  the  words  before  thi'y  can  intel- 
ligently execute.  Workmen  are  constantly  obliged  to 
work  thus  under  dictati(.n,  —  to  interpret  words  by 
forms,  and  to  use  tin-  imagimition. 

Caud-Exkkcisk  in. 

Squares  on  Diameters  and  Diagonals.  -  Zir.  £aii  MouldlnR. 

Draw  a  square  on  its  diameters.     Using  the  di- 

anietera  of   the  first  square   as  the   diagonals    of    a 

second   square,    draw    the    second    inside    th.'    fir.->t. 


4«( 


TKAVllKHs'   MASCAL 


Tliirt  ffivi'M  two  conct'iitrif  M|imn'M.  IIilvin^{  tlivi'l^'tl 
tliii  hIiIi'h  III'  till'  tiiidr  M|tl;irit 
into  lour  |i;irfM,  ciiiini'tt  fli« 
piiintn  III  (livii-iiiii  \>y  nlilii|tii' 
liiH'H  imriillfl  with  tin-  wiilrn  ut' 
liio  imiir  ^<l|llu^^'.  Tlim  itt  » 
^;<(ii<l  lit^iiri'  fur  tlu>  i)ii|iil«  to 
iini\ly/«'  lifforo  tlit-y  lii't{ii»  '" 
ilriiw  it. 

Ziii-ZAii  MoiLlMNd. —  Draw 

^ two    iiiinillil    linri/.oiitivl    liiuK, 

..I  Hutlioifiit  i.i.Ktli  to  nllow  tliiTc  or  inon-  hiiuiui'm 
to  ill- ilriiwii  lii'twi'fii  thfiii.  Divi.lr  til.'  ujipiT  silk- 
of  »'iu'h  H(|iiur<'  into  two  cqiml  partn,  nint,  from  tlio 
poiiitrt  of  division,  draw  tliu  oMinim  liii<'«-  Ailil  a 
line  aluivf  ami  a  liiic  below,  jiarallul  with  the  Hi.l.-H 
of  till'  Htjiiari's. 

('ARii-KxKit(  iHi;    iV. 
A  Pioture-Frame. 

Draw  an  oblong,  with  its 
wiilth  fiiual  to  two-thiriln  of 
itM  hciglit.  Divitli"  its  wiilth 
into  nix  I'liual  parts;  draw  tin! 
vertical  lines  1 '-'  and  .'»  4  ;  and 
then  th<'  horizontal  lines  f)  0 
and  7  S,  forming  sipiares  at 
tlie  corners  of  tho  ol)l')ng. 
Draw    the    diagonals    of    the 

^^^__^_^^^_ small  Hiinares;    then   add  the 

hliort  vertical  and  horizontal  lines,  which  divid.'  each 
side  of  tho  frame  into  two  ciiual  parts. 


1 


>  /  K. tin  III  1,1. \K  nui'itt:s. 


i; 


Iiiviii^  iliviil<>il 
!•  oiittr  Miimrii 
I,  I'liiini'i  t  til*' 
inn  )>,v  <ili|it|ti« 
ill  tin-  i»iilt'H  of 
If.     TliiH    in    II 

'    tl»»     J»ll|lilH     to 

tliry  bfjjiii    l<» 

■LDINO. —  Draw 

ori/.oiitivl  liiii'H, 
ir  inori-  H(|uiirfM 
tlic  \\\t\wx  niile 
,  niid,  from  tlm 
)  liiicrt.  Aild  a 
I  with  till!  Hitli'M 


)hl()n^,  with  its 
()  two-tliirtls  of 
livith'  its  width 
jtiirts  ;  draw  tho 
.  '1  and  .'{  4  ;  an<l 
zontal  lines  5  0 
iiing  miuarcs  at 
of  tho  ohloiiR. 
iagonals  of  tho 
;  thi-n  add  thn 
■liicli  dividi'  likth 


r.Mii»-Kxf:m  IHK.  V 
OblonR  IIoui». 
jlraw  ail  olilninx  <'<|inii  to  two  ri|iiiki  hi|iiinf<.  'I'li  <U 
tlii-.  Iii>t  draw  ii  virliial  liin' 
of  till'  rr(|iiirid  iciii^lli,  —  two 
inilii*.  I'nri'Xiiniidi';  lii<'iidr;iw 
iVohi  ciicii  rnd  a  liori/.onlal 
line  to  till'  right,  twii:<'  a^ 
long.  C'oiiipli't*'  till'  ohloiig, 
and  draw  its  diaiiH'ti-rH.  'I'Ih' 
liiiglil  of  tlu'  roof  is  (>(|iial 
to  one-half  of  tho  height  of 
the  olilong.  It  should  |iroje(t 
sliglitly  at  eacli  end.  Notiee  that  the  horizontal 
diameter  of  the  ohlong  giveK  tho  tojw  of  the  door 
iind  of  the  lower  windows.  Add  the  windows  imd 
chimneys. 

Cahd-Kxkiicisk  VT. 

Oonoentrlo  Bquirca. 
Draw  a  si|uare  on  its  diame- 
ters. Using  the  diameter> 
of  tho  first  Hquaro  for  the 
diagonals  of  a  second  s<|uare. 
draw  tlie  Becond  square  inside 
the  lirst.  Divide  the  senii- 
Miameter.H  of  the  first  square 
into  two  parts,  and,  through 
the  points  of  division,  draw  a 
third  sipiare.  Krase  the 
dotted  lines. 


1 


m 


UAtllKlif    Mi  MM.. 


Vnscr.sruv  Swi  aickh  i.ukxhi.  l|nuiz..NtAi.i,v,     i 
—  I»raw  t«..i..trullrl  l.on/...iiiul  I......  ..I' .u.y  .U^hhhUmI     | 

iHiKtli.  ""'I  'I'vi'l-  »!"•  iiit«TVi-nii.«  «l»ivv  int..  i..iii..n».  | 
Dniw  «h..  .liiu«.-t..r*  ..f  tl..^  m,i.ar.-.  un-l  tli.n  .l.vi.l.. 
...mI,  H..n.i-.liunM.t.T  int..  tw.  i.irl..  Tl.r...,«li  tl.r 
,,oi„tK  of  .liviM-.i,  ..„  ll...  m-...i-.l.um..t.T-.  .Imw  ofT.-r 
,.,uun'H.  Km.»«  tli.m..  piirt..  of  lli..  diuin.t.-r.*  ..f  IUm 
lur«.T  ..i-mn--  wl.ifl.  lull  witi.i:.  H..-  Humll.r  m,uur.'.. 

TIk'h.-    rl«lit-liiM'    llu'tifM    iiiv    I'lit    u|.j.lio«ili..iiH   ..r 

|,n.vio.i.  1.-..!.".  II'  '•<•>■  "f  »''••'•*  *■•'»« """'  "'"  "••* 
uii.h-M.KMl  l.y  tl.-  impil-,  r-IW  HuMi.  I.,  th.m.-  .-s.-r- 
ciHfM  wh.Ti«  tluy  w'l.-  lliHt  .Iriiwu  uii.l  .xplmn**!. 

('Ann-KxKiiri»K  VU. 
A  Pour-polnud  Bt.r  fornn»<l  by  A  Squwo   •nd  U<ma*\9» 

Uraw  It.  B<]uurf  "f  uny  <li'tl- 
iiitf   HI?,©,  anil    tlH>n   n.ia    itji 
ilianiotiTH.     Iliilvf  tlio   51'iiii- 
.liiiuietcrs,  thiit  ii*  ilividf  tlirin     t 
into  two  iMjUiil  imrtH,  itml  cm 
tla'pointfof  «livi»i<iin'«iiiHtni('t     ; 
ft  a(|iuir»'.     On finli  xu\i'  <>*  tlit; 
liiHt  H(|imr«',  tlrikw  uu  isow«'lej.     | 
triftn^l*,  with    itH  niH'\  in   ii 
coriiiT    of    tlio    flrHt     miimr.'. 
Knt-  tiM-  fli-Ht  M|Uiin-  uiul  its  diunH-tiTH.  i.wlhat.Ml  l.y 
,l„tt.a  lines  in   tlu-  o^.y.  m<\   tl.er.   is   IrH   h  iout- 

ixiiiitiMl  »tiir  , 

Cull  til.  uti.'.iti..!!  of  tho  l.upil«  to  tho  «ynun..tru-id 

urrann'-nu'nt    of  the    linen  .ilH.ut   the  eei.tre   ot    tho 

H.inure.     Show  them  that  when  they  have  drawn  one 


I 


i 


4 


OIII/liNTAII^ 

any  <U"iKi'i»'«''l 
•«>  ititi>  i><|iiiiri^> 
1. 1  tlii'ii  iliviilx 
'riimngh  tin- 
••rx,  «lmw  uiWif 
miintt'r>»  rif  tlif 
uullir  i«i|imr<>». 
iH.|tlii:«iii<iii«  ••' 
■uturci*    i»r«>  not 

tit    tlHWt'  V%"T' 


tn    •nd   IlO«9«tM 

lun*  "f  luiy  ili'll- 
I  tlu'i)  iM  \i* 
liilvi"  tho  si'Mii- 
d  it*  (lividf  tlii-rn  j 
ill  jnirti*,  iinil  "ii 
liviHitiii  miiHtnK't 
I  finli  Hiii"'  <>*  tl>" 
I  raw  lilt  iiO«f»ilH!» 
li  itrt  iipi'S  in  (» 
Ir-  lifHt  K.|Uiirt'. 
ers,  iiiilivatiMl  l>y 
u  Ih  Iffl  »  «u»ir- 

)  tho  xyiiiim'truNil 
lu)  i:t'iifie  of  til" 
\'  luive  ilruwu  ono 


1 


lllio    lll.y    MlllftI    .iiltW    fi'Hllill    "tll'T    llIM'*    liuviiiK    ill*' 

ii.iiin»  |..mitioii  witli  rif*T<iMf  to  til"'  ••••nirf  ••»'  tin-  Hu* 
nn*.     It  will  l»M  fuiiiiit  KjMM  iiilly  »«'r\  i'l'iiMi-  m  tli<lii- 

lion  fXiniM'*,  lliii'*  l"t  iM:il<<'  n I'  tlii'  fiin.liinniii.il 

|iriiMM|'l«'  itl'iLxiHii,  — ".vimn.'lriftil  i«rn»n«i'nM'Ut  a'miit 
II  c»'iilr«'. 

•  "XUP-KXKIM'HK    VMI. 
A.  tlooa*  tad  Poroh. 

I»riiw  li  r"|ii»n'  lor  tln'  liody 

of  llir  lin  'Hf.     Prcm  til '  'fiitri' 

of  tint  iijUM'r  Kii|i>  iif  tin-  hnimri'. 

ilmw  !i  liiu'  vijiwiinU,  •■•jutil  to 

.ii>!-httif    of    til"   »iil»'    of    tht 

■<(i»aic.     Kroiii  till'  to|t  of  thic 

liiir,    draw    iIh-    iiiinT   oliliiiuf 

liiicM  of  tin-  roof,  ami  tlioii  tin* 

lUitur    purallii     oliliijii.'    liiici'. 

Xotici-     tliat     tin-     r.Hif     i>ro- 

j«'ct«   ln-yonil    tliu    ci  l.'H   of  tlii<   liointo.       Miiki-  tlio 

titiiiuu'y  iiM  lilyli   iw   till'   riiln<'   of  tlu'    roof.      Hn 

tli<-    otiicr   niilf    of    till-    riHif.    tiraw    tlu'    lioiizmilal 

atxi   vi'i-ti.al    liiUH    fi.niiiii>,'    tin-    |iroj.'.ti<.ii    tor    flu- 

window,     I)ivii'iii>;  tlm   oitlf   of    liii-   nwif    into  four 

•■<|iiul  l>artn  wiil   «ivi>  jioiiifs  wIhtu  IIh'  liin-  i<\'  tin- 

^'ulilc  hiriki'  tilt-    rocif.     'I'lu-    ImhIv    of  tiir    |ii>i<  li    l* 

fiirnii'il  I'y  a  M|uai>'  iliawn  <»ii  oiH-liulf  of  tin-  lifi>{lit 

(.f  tho  HJilr  of  tlif  Iioii-.('.      Till-  roof  i.f  tin-  porth  in 

half  as  hi^'h  aft  the  l"i'ly  of  tlic   ponh,  und   pr-ji'itK 

Nli>,'liHy  li.-yonl  thi-   l'"dy,      l»lvid.'  tl.c  ii{'|i<->-  liidf  of 

til.'  Iiody  t>f  tho  jKm-h    into  four  partH.     Thf  iowcr 

window  of  tin-  liody  of  thi-  liouxf  is  h:ilf  tlo-  lifijrht 


\ 


IKAVHUHi*'    W.I.V/'.I/. 


i.r  tin-  li-'M*''.  wfill.-  llu'  wi.hli  ..f  tlif  wfii.L.w  I- 
liikir  'tf  it»  ImIkIiI.  'I'll''  <liiiuhi.iiiii»  ..f  tin-  ii|>|nr 
wmhImw  iir<'  ii  litllf  li""«  «lt*ii  ••»"""•  •••  <'"'  '"*'■'  '*''•'• 
ilow. 

It  i«  ii«>t  •■>  '»'  'Xi l""t  'I'l'*  viitiiiiii  iliiMnii  Mill  .il 

llr«»  rt'iulily  iiiMi|irtlit'ii<l  (Ik-  Mirmux  iiifu«iii'.iiMhl«  of 
tlii.  .•x.riUi'.  It  will  Ih«  i»iil!l«ii'nl  if  iln-y  ((«t  an  iti.u 
«f  llif  iMitlt'Ml  of  •iniitfriiftiiin  II  ilrinviii;?  liy  propor- 
tion Till*  ixi'rri»-  bIioiiIiI  Im-  ilruwii  ii»  luru'*  ii*  "ir* 
i'UinHtiiiii-fi>  will  ptriiiit. 

Cakd-Kxkih  l-K,  IX. 

Brcot  Orott. 

Praw  a  Hipiitn,  iumI  iliM<li' 
i-acli  of  ill*  niilt'i*  into  tliiriU. 
(!oniH«t  tlif  point*  of  ilivi»ion 
liy  fwii  vrrticiil  ami  two  Imri- 
/.o'ltikl  li!li•^  tIniN  f(>rinin((  niio* 
H(|iiari>>*.  KiiiKf  tln'  rfiilrul 
«<(piiiri'  mill  null  <orii<'r 
s(|iiiiri' :  in  otlicr  wonln.  t'rii»<' 
the  liiif'*  wliiili  iiif  iliiliiil  in 
till'  fopy. 

Tliiwc  lini'K  whiili  un-  .Iniwn  to  lii'l|i  in  tlif  .on- 
Ntrii.tion  of  till'  IlKurim,  uml  xo  ur.'  ^omi-tiini'H  I'uU.'il 

•■toiistrm-tioii  lini'K,"  urc  uhvay»<  to  I la-cd  wli.ii  tin- 

ilrawiiiKi  ar.'  llniMln'il.  Tlicy  aiv  tin-  .lottiil  iim-«  of 
till'  copii'M.  Li't  it  lu'  ri'iiit'iiilitTiMl,  tliiii.  tliat  tlicm- 
lini"«  art"  ulwiiyj*  to  l«'  rraMfil 

'I'lii*  cxi-rrixi',  with  Hoim-  Hli|,'lit  lulilitioiiH,  hihIi  an 
tlif  iliimonaU  ot  till-  siiiull  HtpiartM,  will  iuihwit  w»-II 
for  a  ili  •tiitioii  txi-rti^f. 


HlUMfilll  USh  H'il  NK" 


.•»l 


if   tin-    iipiifr 
n«  lowi-r  win. 

lililrvii  Mill  .il 

kxIM'i'llM'lltx  III 

•y  ^I'l  iin  iiU'it 
I*  luru<'  Ik*  'ir- 


I',  uml  iliNiilo 
»  ititi)  tliinlfi. 
if<  (if  division 

llll<l     t»<)    lloli- 

t  r(>rinlii((  niiH* 

'       tllf       iM'lltl'ul 

ciicli  citriKi' 
r  wiiiiIh.  t'rii»<' 
lire  i|(ili<'i|   ill 

•l|i  ill  tllf  loii- 

ll|l'tilll)-M    i'llllol 

ni-<'il  wIm'Ii  tllf 

llnttfd  lillfH  of 

ifii,  tliiit  tlit'sf 

itiilllN,  ilUfll     liM 

ill  uiidWfr  Wfll 


I 


A  OroM  forniad  of  fiM  Hijumm. 
I»niw  u  >M|iiftr«'  irti  »t» tliuiiiflf r«.     Divitlo  ciuli  of  if« 
niilcH    intit     i'oiir  i'<|iiul    |iurt> 
Divitif      till'      «'Mii-<liuiiMtfr» 
liilo   two  «>i|tiiil   part*.     Con* 
IM>rt  til)'  |M)iiiti*  )if  iliviiiiih  UM 
ill  tin-  lopy,  uimiiit?  to  iiuikf 
till-    ihtfr«fitiii(i{   liiit'<  iif  tllf 
i'M«M  iiiPi't    itt    till)   pointit    lit 
ijivixioii      oil     tllf     iliiiiiiftfix. 
Ill    iitlifr  wiiriU,   (oiiiifft    llif 
|K)inti«  of  itiviitiiiii    liy  iililiijiif 
jliii'ii,  MO  ikM  to  form  Hvp  obliqiiM  iii|uur«fii  itiNidt)  tin-  lirxt 
i«i|uari>. 

('MII>-l!xKllt'M|.:    XI. 
Two  OblJDiii  m  •  Bquar*. 

Driiw  II  «i|iiurf,  ami  ilivido 
itn  KidfM  into  thirds.  Tliriiii((li 
the  jKiintH  of  division,  dmw  two 
vfitiful  mid  two  lioiizoiitiil 
liiifs,  iiiitkiti^  iiitif  >t<|imrf:4.  In 
fiu'li  foruf r  Hqiiuri',  draw  a  di- 
a^oiiul,  with  itn  nidf  towards 
tllf  fftiti'f  of  tllf  largf  s(|iiaro. 
I<»(<tly,  draw  litiCM  foniifctiiig 
tlu>  «'IiiIm  of  tllf  diai^oiialf,  wliicli 
art'  jmriillfl.  Tlif  tfadifr  can  tmHily  modify  tlii* 
t'Xfrcisf,  and  iiiakf  a  dictation  lc^.  uii,  l>y  adding  othfr 
lini'rt  parallel  or  oliliijue  to  tlioMc  ali-fady  drawn. 


r.'.» 


TKACUKH.S'    MANUAL. 


Caud-Kxkim  rsK.   XII.  1 

A  OrOB«  with  iU  AnKles  aU  Acute. 
Draw  a  square,  and  .livid.-  »'a.-h  of  its  sid.'s  into 
thirds.  Tlirou^li  the  points  of 
division,  draw  horizontal  and  j 
vortical  lines,  fonninf,'  "'»" 
snialliT  squares.  Divitle  each 
side  of  the  inner  square  into 
halves.  In  eaeh  corner  s(iuare, 
draw  a  diagonal,  with  its  si.h^ 
to  the  centre  of  tlie  large  sfjuare. 

^roni  each  end  of  each  diagonal, 

draw  a  line  to  the  nearest  point  of  division  on  the  inner 

square. 

Oaku-Kxkkcisk   \1U. 

Bigbt-Iiine  MouldingB. 

FouM  ".  —  Draw  two  pai- 
allel  horizontal  lines,  at  any 
.riven  .iistance  apart.  Divide 
the  .space  between  them  into 
squares,  and  .Iraw  the  diago- 
nals of  the  squares.  Add  a 
horizontal  line  above,  an.l 
another  below. 

Form  /'.  —  Draw  two  Iwri- 
zontal  lines,  at  any  given  dis- 
tance apart.  Divide  the  intervening  space  into 
squares,  and  draw  their  .Uagonals.  D.vide  each  halt 
ol  semi-diagonal  into  two  equal  parts,  and,  through 
the  points  of  division,  draw  the  inner  s.iuar.'s.  Add 
ii  horizontal  line  above,  and  one  below. 


>  lit  A  ui  II T- 1,  is'k:  Fi'ir  It  /.  ^ 


m 


ute. 

its  sides  into 
1  tlu'  points  of 
lorizontal  ami 
Ibnning  niii" 
Divitlo  t'licli 
(r  sqiuirc   into 

coriu'r  s(iiuirt', 
I  witli  its  side 
iolar)^es(iuurf. 
fcadulia'^onal, 
on  on  tlio  inntT 


Draw  two  pai- 
1  lined,  at  any 
apart.  Divide 
vot'U  them  into 
raw  the  diago- 
uares.  Add  a 
le     above,     and 

Draw  two  hori- 
t  any  given  dis- 


ing    space 


into 


)ivide  each  half 
ts,  and,  through 
r  scjuares.     Add 

V. 


l-'niiM  <•.  —  1  >raw  two  horizontal  lines,  at  any  definite 
distance  apart,  and  divide  the  spai-e  l.etween  th.^m  into 
squares.  Draw  their  diameters  ami  diagonals.  Di- 
vide each  semi-diameter  into  two  ei|ual  parts;  and. 
from  the  points  of  division,  ilraw  lino  to  the  sides  of 
the  s(|nares. — these  lines  to  he  parallel  with  the  di- 
agonals.     Adil  a  horizontal  line  ahove.  and  one  helow. 

A  r.\<ir.  or-  IvHiht-Lim;  KifirRi'.s, 
It  is  intendi'd  that  the  drawing  of  the  (common  ohjects 
given  on  the  following  liagc  shall  he  intcrspcrsc(l  with 
the  other  exercises.  These  forms  are  to  lie  drawn 
without  directions,  the  teai-lier  putting  them  o?i  the 
hoard,  and  the  pupils  reproducing  them  on  their  slates. 
Observe  that  round  as  well  as  rectangular  ohjeets  are 
repre.stMjted  by  the  straight  lines.  Similar  outline 
drawings  of  other  objects  may  he  reaiiily  added  to 
these.  When  doing  the.se  exercises  the  principal 
lines  shouhl  be  drawn  first. 

Thus  far  we  have  worked  with  iigures  composed  of 
Mtraight  lines  alone.  I5y  this  time  the  names  and 
character  of  straight  lines,  and  of  various  straight-line 
Hgure.s,  .should  be  ILrmly  tixed  in  the  minds  of  the  pu- 
pils. The  next  exercises  will  include  curved  liiu's, 
the  drawing  of  which  will  give  more  varied  ami  inter- 
esting prav^iee. 


Questions.  — What  is  siiiil  of  ro(iiicii«ii  mul  niliiiKcmunt  in 
drawin;;?  Of  class-analysis  of  forms  Wloir  lic^jinninw  to  .liaw 
them  f  DescrilH'  memory  aruwint,'.  What  is  its  use  '.  When 
are  siinares  sai.l  to  he  concontrio  >  What  is  the  nse  of  the  ilotted 
lines  in  the  ciipies  >  ami  what  is  to  1)0  done  with  them  ! 


6* 


CM  APTKK     III 

SIMPLE  CUUVES. 

Ik  the  pupils  have  been  interested  in  the  prece.lii.); 
exercisen,  they  will  he  nm.-h  more  intereste.l  .n  the 
oneH  which  follow.     It  is  rare  to  f....!  ch.hlren  that 
do  not  like  to  draw.     As  «oo:.  as  they  acquire  a  litt  e 
skill  in  the  use  of  their  pen.^ils,  they  delifiht  to  apply 
it  in  every  direction.     While  they  shoul.l  he  allowed 
great  freedom  in  the  exercise  of  their  skill,  the  tea.her 
Hhould  frequently  require  them  to  submit  the.r  uue- 
p,.,ident  work  for  inspection,  in  order  that  the  faults 
may  be  pointed  out  and  corrected. 

A  Curve. 
A  nirved  line  is  n  In,.  n-Uirh  rha„rs  Its  direction 

at  t'iwri/  point. 

Curved   lines   are    of   diflerent 

kinds. 

A  SiMi'i-K  CriivE.  — yl  s!)ii]d<'. 
curve  henils  reijiddrl;/,  and,  if 
continued,  irifl  form  a  rirrh: 

All  simple  euvvea,  less  than  a 
circle,  are  but  parts  of  a  circle. 
The  curves  at  A  are  simple  curves. 

The  teacher  should  have  suitabl.-   ..l.je.ts   U>x  the 

I 


m 


TKACIIKUS'   .\tA,\L'AL 


linrpiisc  ot  illustrating  the  diflcrt'iit  WrniU  of  ciirvcH. 
In  till'  set  of  nioih'ls  for  priiiisiry  schools,  thcri'  is  a  ilisK 
witli  wliifii  tlif  various  fcatiiros  of  the  tinrlc.  or  parts 
of  cirrlcs,  nv.iy  Ix'  iilustratcil. 

Hiivin;,'  (Iriiwn  several  simi»li'  curves  on  the  lioaril. 
and  pxi)lain<'(l  thcin  to  tlie  pupils,  require  tbo  latter 
to  draw  from  memory  a  rij^lit  unRle,  and  then  to 
connect  the  two  ends  of  the  lines  forminjj  tlii'  alible 
hy  a  simple  curve,  as  at  I». 

Tliis  figure  is  called  a  tiuadrant,  i>ec,ause 
it  is  ()iM'-(iuaiter  of  a  circle.  Kepeatinn 
till!  curve  to  tlie 
left,  we  have  a 
semi-circle  (C),  or 
one-half  of  a  circle.  Kej)eat- 
ing  the  lines  below,  w((  have 
the  complete  circle  (I)),  with  O. 

its  liorizontal  and  vertical  di- 
ameters. 

To  draw  a  semi-circle  (('), 
begin  by  drawing  a  liori/.ontal 
line ;  at  the  centre  of  this,  draw 
a  perpendicular,  ecjual  to  one- 
half  of  the  horizontal  line. 
Connect  the  ends  of  these 
D.  line.s  by  a  sinijde  curve.     To 

draw  a  circle  (D),  begin  by  drawing  two  of  its  diame- 
ters, tlie  same  as  for  a  square  ;  then  connect  tlie  ends 
of  these  lines  by  foiir  simple  curves,  which  will  form, 
when  all  drawn,  one  continuous  simple  curve,  or  circle. 
It  is  not  to  be  expected,  at  fir.st,  tluit  pupils  will, 
in  this  way,  draw  a  circle  with  any  great  degree  of 


HISII'LK  VVRVKS. 


iiis  of  ciirvcrt. 
tlnTc  is  II  disk 
■\ti'\i',  or  parts 

III   till'  liniiril, 

ii'<'   till*   latter 

mill  then  to 

UK  till'  aiigl<> 

Iraiit,  IfL'iuiUHi! 
Kt'licatiiiK 


O. 

1(1  vertical  <li< 

mi-oircU'  (('), 
g  a  liori/.oiitiil 
•(n)f  tliiM,  ilraw 
t'Hual  to  oni'- 
iri/ontiil  liiii>. 
ids  of  thcsi' 
1»^  cvirvo.  To 
)  of  its  (liamc- 
iiiect  the  ends 
icli  will  form, 
jrve,  or  circK'. 
it  pupils  will, 
cat  dt'grei'  of 


( 


acfiiracy.  Iiidfed,  it  is  not  Iutc  given  so  imuli  as  an 
i-xtTiMsi'  to  be  copied  liy  the  pupils,  us  for  tlie  purpose 
of  showing  tliem  the  completion  of  a  simiile  curve. 
—  showing  that  all  simple  curves,  if  continued,  will 
form  lireies. 

When  a  curve  is  drawn  on  a  Rtraight  lino,  as  ;il 
K,  the  straiglit   line   is  called  the 
Itase  of  the  curve,  while  the  dis- 
tanco  of  the  i-urve  from  its  Imse 
is    called  tlie  altitiiile.  or  heighl.  B. 

of  the  curve.  The  dotted  line  in  K  shows  the  alti- 
tude of  the  curve  at  its  centre. 

It  is  important  that  pupils  have 
a  clear  idea  of  the  hase  and  alti- 
tude of  a  curve.  The  hase  is  a 
straight  line  connecting  the  ends 
of  a  curve  :  it  may  he  vertical,  lior- 
izoiital,  or  oblique,  as  shown  at  V.  *"• 

\Vc  do  not  say  a  vertical  curve,  or  a  horizon- 
tal curve,  or  an  oblique  curve ;  but  we  descrilie 
curves  by  their  base  lines,  as  "  a  simple  curve 
on  a  vertical  base."  or,  "a  simple  curve  on  a 
horizontal  base,"  &c.  The  altitude  of  a  curve,  or 
of  any  point  of  a  curve,  is  its  perpendicular  dis- 
tance from  the  base.  It  will  be  remembered  that 
perpendicular    does    not    necessarily    mean  vertical. 

Hence  every  curve  has  altitude,  whether  its  base  line 
be  horizontal,  vertical,  or  oblique.  If  a  curve  has  a 
vertical  base,  tlu'  distance  of  the  curve  from  its  base 
is  called  tlie  altitude  or  height  of  the  curve,  just  as  if 

t  had  a  horizontal  base.  When  we  simply  speak  of 
the  altitude  of  a  curve,  we  mean  its  greatest  altitude; 


ftH 


IKM  tlEKS'   MASUAL. 


l.iit  WO  may  him-hU  of  itw  altitude  at  any  point,  Lesiilrs 
till-  hinlu'st,  jirovidi'd  w  fli'siRnatf  tlui  point. 

Draw  on  the  l.la.^klioar.l  .-irvi's  with  vi-rtiiMil.  hori- 
Koiital,  and  ohliquo  hanoH,  and  witli  their  c^ntrcH  at 
dil^ViTiit  iiltitnd.'M,  until  pupils  have  a  clear  eonipru- 
liensioi:  of  the  terms;  for  these  terms  will  be  fre- 
quently used  in  sueceeding  exercises. 

In  the  page  of  skeleton  letters  will  Xw  found  some 
good  forms  for  hlacklward  copies.  As  the  letters  afford 
the  simplest  combinations  of  straight  lines  and  curves, 
and  as  the  forms  are  familiar,  no  definite  proportions 
need  be  given  here :  they  will  be  reiwlily  discovered. 
If  the  subsequent  exercises  should  be  interspersed 
with  the  drawing  of  these  letters,  it  will  give  a  pleas- 
ing variety  to  the  work.  Not  too  much  of  the  same 
thing  at  one  time. 

A  Cnun.K.  —  A  rlrc/e  in  a  plune  fig- 
ure houndeil  hij  n.  nirvi'd  lliin,  mffed  its 
chrniiifi-ri'nre,  every  part  of  irfiich  ia 
e'/ml/i/  Jlst'int  from    a  point   within, 
jj,  called  its  centre  (ii). 

This  is  the  strict  mathematical  definition  of  a  cir- 
cle, and  makes  it  consist  of  the  spacio  ench.sed  by  the 
curved  line. 

A   Radiis.  —  A  radius   of  a  circle 
Is   a   sfrai;//it    line    drawn   from    its 
centre  to   the  cirruniference  (H). 
When  we  wish  to  speak  of  more  than 
^^  one  radius,  we  say  radii.     A  circle  may 

have  an  unlimited  number  of  radii;  that  is,  you  may 


point,  iK'niilfH 
|)oiiit. 

verticttl.  liori- 
u'ir  centrcH  at 
I  cl«'!ir  coinpri!- 
18  will  be  frf- 

!)(•  found  Homi' 
le  lottoM  affbnl 
ties  and  curvnH, 
litp  proportiotiH 
lily  discovered. 
)e  iiiteri^persed 
ill  give  a  pleas- 
Bh  of  the  «ame 


iH  a  plane  fig- 
line.,  mlfad  its 
rt  of  which  is 
point   within, 

inition  of  a  cir- 
enclosod  l»y  the 


Ins  of  a  circle 
•awn  from  its 
•rencc,  (H). 
sale  of  more  than 
i'.  A  eirclo  may 
that  is,  you  may 


SDtl'l.h:  rdltVKS 


r.<» 


6i» 


IK.UIIhns-    M.XSVAI,. 


unlimiti'il   mmibor 


(Iniw  liny  number  of  riulii.  suid  yet  thoro  run  Ix-  am' 
iniirt'  tiriiwn  iil'ti-rwanU. 

DlAMKTKR  OK  .\  I'lUrr-K.  —  .1  iH'iiiirtrr  of  n 
I  Irrlr  is  II  xti'iiiijht  lliii;  th'inni 
f/iriiiiij/i  till'  niih'i'  mill  turn  If 
iiii/  fill-  lininiif'i'i'iK'i'  "II  f"if^i 
siilr.t   (])). 

Ailiiuii'trrof'arir.lfisiiiiiilo 
lip  of  two  milii  riinninK  in  op- 
poHitd  ilirt'ftionf'.  TIkip  may 
l><)  ivn  uiilimitr.l  numl>fi<if  di- 
iimfti'i-.x.  iiM  tliric  may  In*  iin 
.f  radii.  Hiulins  nu-aiin  si.okf; 
dimnctcr,  tliiit  wliiidi  mfa.surfs  tlimunli. 

Those,  tlten,  are  tlie  features  of  the  eirele  :  Tlir 
arrnwfrrriin;  whieli  Lends  e.|Ually  in  all  its  parts; 
tlir  ii'ntvi;  w'.iieh  is  at  th.-  same  distance  from  every 
p..int  in  the  eireiimferenee ;  tin'  rnillii.",  or  distane.< 
from  th<'  centre  to  the  circumference;  tin- ill'iniito-, 
whicli  is  tlie  longest  straight  line  that  can  he  drawn 
ill  tlie  circle,  and  divides  the  circle  into  halves,  callfd 
senii-circli's. 

In  popular  usa_!,'e.  the  word  "circle"  in  often  em- 
ployed simply  to  in.licate  the  curvc.l  lijie  hounding 
the  circle,  and  miKht  he  detined  thus  :  — 

A   rirrli'   is   an    nnlli-ss   ciit'iril  liin;  n'lii'li  li'ii<l» 

l/Hlllll/  ill  ifl'l'l/  JKll't- 

Ciinun  AM»  \ho  of  a  Ciitn.K.  ~  A  straight  lino 
which  touches  the  circumference  of  a  circle  at  two 
points,  hut  i»  shorter  than  the  diuinetcr,  is  called  ft 


orv  can  Ix'  one* 


'I'lltirfiW  of  ii 
/lit  I  tin;  tifiiini 
tfff  iliiil  tnili'/i- 
^'I'l'riii'i'  oil   liiilli 

ai'inlf  is  mini*' 

running  in  op- 

is.     TluTo  may 

I  iMiml'fi'it'  tli- 
•ic    may  l"'    iiii 

iiicaiiH    HjHilic; 
h. 
lie  cinl'' :    '/'/"' 

II  all  its  parts  ; 
niict'  from  every 
iiix,  or  (Ustniice 
■ ;  till'  tliiniiiffi; 
at  can  Im-  ilrasvn 
to  lialvcs,  I  iillcil 

i- "  is  often  eni- 
il  lino  bounilinj^ 

in;  ti'h'ii'li  biiiiln 


-  X  Rtraii^lit  lino 

a  circle  at  two 

aetor,  is  called  a 


snil'LK    VIHVKS, 


r.l 


clioid.  Tt  divides  the  circle  into  two 
iiiiei|nal  jiarts,  either  of  whii  h  is  called 
un  arc.  In  drawing',  the  chord  is  usuuU 
iy  calieil  the  hase  of  ll tirve. 

Whenever  children  iiro  given  dellnilions.  the 
detinitions  clionld  he,  if  possihle,  otrictly  accu- 
rate, that  there  may  bo  nothing  to  unlearn  after- 
wards. The  mope  of  the  deliliitiohs  r.|iould  he  re- 
peatedly pointed  out  and  illustrated.  In  the  preMent 
instance,  the  mathematical  ilellnitionof  a  circle  nii^ht 
be  illustrated  hy  .i  penny,  while  the  popular  u>a;,'e  of 
the  word  might  1"'  ilhi>trated  hy  a  ring.  In  llu* 
one  case,  the  whole  (tf  the  penny  wouhl  represent  the 
cinile ;  in  the  otlu'r  case,  the  circle  would  he  repre- 
sented by  the  ring.  Thus  'he  distincli.m  l«etweeu 
the  two  usages  of  the  word  would  1 learly  seen. 

Tin'  pupils  should  111'  reipiired  to  name  objects 
which  are  circiilar  in  form.  They  would  doul>th'ss 
mention  wheels,  hoops,  plates,  &c. ;  ipiite  likely  they 
would  also  mention  balLs,  oranges,  pencils,  &c..  because 
thost!  objects  have  the  elenicnt  of  rcMindness.  .\t  this 
point,  thiTcfore.  it  woidd  be  well  to  give  some  special 
attention  to  the  wonl  "round."  It  is  a  long  time 
before  children  learn,  without  sonui  special  instruction, 
the  exact  force  of  this  common  word.  Various  ob- 
jects they  can  only  de-crib"  as  round,  though  their 
forms  nuiy  <litl'cr  in  a  marked  degree.  Thu.-,  a  circle 
liko  a  ring,  a  circle  like  a  disk,  a  sphere,  a  cylin- 
der, a  cone,  are  ail  round,  anil  nothing  more.  Hut 
with  a  few  illustrations,  repeated  several  times,  they 
soon  compreheml  that  the  word  "rouinl"  is  insuf- 
ficient to  describe  all  objects  wiiose  tonus  have  the 


IK.trilH/f'    MAM  tl.. 


mU'IiiiiiI  of  riHtii.liH'K*}  iiinl,  wlifii  thf  ilintlm-litinn 
bftwci'ii  till-  iil.jift*  ari'  Kiirv  i'l<'!ul,v  »*»'«>n,  tlu-y  n-inlily 
It'iirii  to  ii.>n'  tlif  woriU  wliiili  f)nu'»l.v  «'Xi»r<'i.ft  tlu-i«(» 
tliHtiiictiotiH 

C.viili-KxKHrMl-:  XIV, 
lo«oHb»d  and  C«rouimor»b«<l  Olrol*.  -  Olob*.     WhMl. 

F(»RM  <»,  A  t'irrit'  in- 
.«T«V"(/  I//  11  S'fii'in:  —  III  i» 
|iivvi<iUH  ('xcr«i«f  (l>)  Wf  ilri'W 
tli<<  cinlt'  oil  itrt  liorixoiitui  »ihI 
vcrtiiul  (liiiiiM'td'ri* :  we  will 
losv  draw  II  cii'  Ic  ill  a  K(|u;uf, 
Muviiix  iliiiwii  ii  H<|iiiiri',  with 
t-t  'liiiiiK'tir-i  iinil  iliiip>iiuln, 
iiiiu'k  «>ii  tlif  •Iiii^oimiIh  i»iiiiitH 
iIukiikIi     wlii'li     III'-     ••irilt< 

hIu.uI.I  [<iw.     O'lUM'.t  tlu's.-  iM.iiitM  and  tl U  of 

tl.M  .liiimi'tiTu  Uy  -iiiiplo  <<«rvs.  Draw  tli.-  .iirv.M 
.  an-l'iilly,  M'l'tion  by  sc-tioii.  A  .in-lf  -Iriiwii  iiisi.l.'  >k 
h(|n!uv,  and  lim.liiiiK  tlio  Hcpiaf  ■,  i.-«  said  t^.  l>.  in- 
Hcnlwd.     Knis.'  til.'  dotted  liiK'i*. 

KmUM  /'.  .1  '  '■'•'/''  lii'finnHi't'ihi'il  i(f)i>iit  "  S/iiiifi:— 
Draw  a  s.iiian' ;  tln'ii,  uii  .-aidi  Mf  of  tl|.  .^<i<iai"t'.  draw 
a  wiiiii)!-  .tuv.  Wlini  tli<-  MiiHil«'  <iiiv.'H  an-  unit,  d 
at  111!"  .•..rii.>r>*  of  tl:."  H.|Uan'.  tlicy  nIidiiIiI  for'ii  om 
.■iidli':*^  Miiii.lt'  iiiivf  or  .'indf.  Wlifii  u  «'ir.l<'  i-* 
thus  drawn  arot'iiil  a  s(|u«rt',  it  i.i  waid  to  bo  cirniin- 
^(!ril>t'd. 

FoiiM  ..  .1  (i/olir.  —  Draw  ii  sqimn*  und  it» 
diam.'t.-ra;  th.'ii  an  iiis.ril.cd  .irclc.  Divide  each 
(..■mi-diaiii.'ti'r  and  »'Ul1i  iiuarti-r  Mi  thu  circle  into  four 


i<>  iliMtiiirtiiiiiit 
II,  llii'v  fiulily 


lob*.     Wheal. 

.J  Cirrff  in- 
fiimr.  —  III  i» 
If  (l»)  Wf  ilrcw 

liivfixoulul  uiitl 
tj'rn :  w«»  will 
■li'  ill  ii  c«|iiiuf. 

ii  Hi|iiiirf,  MJth 
uitil  iliiipiiiuU, 
IiiXI'ImiIm  i»iiiiitM 
li  tin-  ciri'It' 
1(1  till'  i'ihIk  «J' 
raw  till'  iiirvi'H 

.Iniwii  iu*iili'  u 


salil 


I.. 


III- 


>i(t  'I  S/imrr. — 
li'  .xijntirt',  'h'liw 
rvi'H  iiri'  iinit«'«l 
lioiiltl  f'or'ii  iiiit' 
It'll  II  rinli'  i.-« 
I  to  be  cirruni- 

iqiian*    und   it» 

Diviilc    cufh 

circle  into  four 


^Itin!  jmrld.     Throui^li  tlin  |H)iPt»  ul'  tlivi»l»ri,  .Ifttw  th« 
iiiiM'r  t'lirvf^. 

KouM  il.  A  MVir/'/,  — .  l»rii«  n  w|iiiiri',  willi  it*  ilU 
ttiiM-ti-rit  ttiitl  .liii({uiiitU  ;  itiiil  tlii'ii  iui  iii»i'rili*Ml  rin-i*'. 
I>iv(t|c  till-  4«>ini-<iiiiiiu'tt'rH  <if  tin-  nftlt'  in»n  t<»Mr 
i  t«)iukl  |iiirtM  \  tliroit^li  tlic  outer  |Hiinti<  of  iiivi«i"ii. 
ilrHW  n  vftroiiil  ••iri-lc,  imkI  rniitlii>r  tliroii^tli  tlii*  iiitM>r 
ptiiutit  of  iliviitioii.     KriiHt'  tin-  tlotfcil  liiin-n. 

I  Cakii-Kxkummk  XV. 

K  Croii  wlt»»  Auitt«i.  itlKht.  Acuta.  »nd  ObluM.  -  fwl 
Moulding. 

Druw  II  («|Huri',  uml  tlivi'l*'  it 
into  iiiiio  t>i|uiil  Hinullt-r  MiuurcM. 
Divide  I'iiih  Midi'  of  till'  iniii-r 
i«|iitu'i>  into  two  (•(|iiid  jhiHh. 
Fri'iii  I'rtrli  jioiiit  of  division  oii 
till'  iiiiiur  Mqimri',  druw  ohlimui 
liiii'M  to  tlif  jioiiitj*  of  division 
uii  thf  rorriHpi}iidiiij{  i«id'  of 
the  liirK'*  i>(|iiiir<-, 

KiiK.T,  Kit  Kkv.  \Jini.i»iN<i. —  Dniw  t!ir»H'  si|niiri'!*, 
«H  ill  ('iiid-Kx'nisf  ill.,  united  hurizoiituUy.  DivitJt- 
tilt'  Ifft  Kidc  of  the  loft  it<]imr«*  into  four  •'«juid  [>iirt*,  j 
Hiid,  from  till-  [lointM  of  divinion,  diiiw  liuri/niitiil  liios 
diviiliny  'dl  the  Hijuari!*.  Divido  tlif  ui»|H'r  Htdi-  of 
«>a<'li  i«i|iiur('  into  four  ••i|ual  |iu,rt(i,  and,  from  tln-u 
(lointK  of  division,  druw  vi-rticid  liio's  tlirouijli  tlot 
squiirc'K,  dividiiim?iW'li  of  the  lirnt  8«|Uiir(  >t  int*>  sixtL'tMi 
Kiiiidlfr  si|imrifi.  Dniw  tlic  liiu'.'*  formiuj;  tln'  frot  as 
hIiowu.      If    llu'    linjtdit    ure.    uiifortiiiuili-lv     without 


1K.it  II KHH'  MAS  If  4 1. 


fiinU,  »li»'i»  tli.«  ti'ftilHT  inu«t  Kiv.«  fur«li.r vi-rl.ul  ix|»li»- 
tiulMMi.  »t  illicfrut.-  ..II  til-  iM.iir.l.  A.I.I  u  li..ri/..ii»ul 
liiM-  uIh.v.'.  iiii.l  in».»thiT  Im-Iow.  'riii*  u  ..II.'  "l"  »li.' 
iii..<'t  |h.|.iili»r.  iw  li  in  •.»•'  »t  ♦•••'  <'l«l«'»t.  ornimifiitiil 
form.*  t.vi>r  iiivt.iiic'l. 

fAnn-KxriuiMK    XVI. 

HoaattM  oompoicil  of  •ImpU  OurvM. 

KoMM  II.  —  Driiw  11  *qinw  ..ii 
ltd    iliuint'fcrs,    iiiul    ui|)i    tin* 
.littH.itiiilH.     ThIiik  I'li.li  Hi'iiii- 
.|iitK.iiiul  UN  11  I'liH.',  tlriiw  u  HJiii- 
ii|i«  .urvc  1.11  I'luli  Hi.K'.     Aim 
I.)  niitki'  all  of  till'  ciirvtm  ttlik»«. 
Ki.uM  /'. —  l>ruw  li  in|iiui.'  .in 
itH tliuiiu'ti'M.  r»>iiiK <'»<li  Hciiii- 
iliimmtor  ui«   ft    littMi-,    .Iruw    i\ 
Hinii.l.'  .'iirvi'  <»ii  I'lu'li  ^iili'. 
FoHM  r.—  Draw  ii  K.jiiur.',  with  Km  .liuiin'tiTM  tuiil 
.liuH.iinU.      r«mK  .'lull  m-mi.iliu«..iml  a«  u  ImH.-, 'liiiw 
II  Kiiiiple  curvit  fuch    niili'.     A<1<1  tl»'  «iiiVfM  on  tlio 
i>«'ini-.liaiiu>t<>rx. 

|.',,,tM  ,/.  _[)m\v  II  H.|uar<'.  with  its  .liuinHiTu  iiml 
,liii«..iiul^.      Widiiii   til.'   m|iiurt.,  ilruw  uii    iiiHcril..'.! 
I'ircU);    UHiiijj  .-ai-li  Hi.tni-tliiiinft.T  of  tho  ciwlw  tt«  ft     | 
biiM',  .liiiw  a  Kiiiiplf  fiii've  on  cttcli  «iilf.  J 

Cahi>-Kxkk«mmk   XVll. 
An  Elght-polnt«<!  StM  »nd  Pr«t  Mouldiiui. 
Druw  a  s.|ii;ir.',  iiiiil  .livi.l.'  it  int..  niin-  .'.lual  f*iiiiill 
h.juai..-s.      Divia."  each  Hi.k  of  thf  central  H»iuare  into 


fUMi'i.^:  mnm 


M 


••r  vi>rl>iil  ixjilu' 

(III  II  Imri/iiiitiil 

la  itiH'  iif  itii' 

imt,  iiriiitiiK'iititl 


lurrM. 

imw  n  i«<|iinri'  on 
nml    uilil    the 

'\tm  (•iK-li  Ht'iiii- 

itnc,  (Iriiw  It  Him- 
lull  MJilt*.  Aim 
Im>  trurvuH  uliki*. 
>rnw  li  ii<|iiui-('  oil 

'hiiiK<'iK'l>  '*«'ii>i- 
huM<s    ilruw    It     , 

I    I'lU'll    Mill)-. 

1    (lillllU'tlTH    Itllll       ' 

I  uri  n  l)UH)',  •Iruw 
i«   cilivi'rt  oil   tll« 

\  (liiiinf'ttTi*  luul 
iw   un    iiimTil»«Ml 

'*••  i 

I. 

Mouldinc. 

line  t'(|iiHl  Miiiiill 

iitrul  ii(|uuru  into 


two  t't|iiikl  |uii'ti«.     rroiii  UM'  |HM  

^j.lr  ni  i1m>  i.nii»ll  .•|imr<'.  <lriiw 

..l.lii|IM<    lilM'<»    I"   Hlllt    |H.illt     Ol 

•|iti>ioii  on  ihf  i'orit-|M>iMlinK 
^i.|..  ol' 111.'  Iur«<'  »\mr'\  V»\uu 

III.'   .|ii»intlt»-«   ol    III »»"»• 

m|iiitri-  IW  .liiiuoiiiiU.  ilriiw  un 
iniMi'  ■'i|iuii'i',  |{iiii.iiil"'i'  tliiil 
ill.'  Imi«  «liiili  'If'  'l"i''''l  i" 
tlif    .'.ipy    ntv    «lwny«    to    !..• 

•'I'Um'il. 

KiiKT  Mnrf.i»i\<i.  —  Hrftw  ii  MTifn  of  i..|iiim'*,  n* 
fur  tl..'  inoul.linu  i;i  ('ur.l-l':x.'r.iH..  XV.  Divl.l.-  t|,.. 
I,  It  M.l-  ..I"  til"  l<'l>  "|"'»«'«-  into  llv.'  ixjuul  i>uit»<,  i.ii.l, 
I1..111  til.'  iiointH  .»r  .li\i«ion.  .liuw  lioii/untiil  liin"« 
tliroii^li  nil  of  tli.»  H.|.iur.>«.     Pivi.l.'  tli.-   iipi-r  -i'l" 

„f  ,',M'li  H.|iiiin'  into  llv |uiil  piU'tH.  uimI.  iVom  lli- 

points  r.f  .livinion.  .Iriivv  v.'iti.iil  liif'*  .livi.lini{  <'u.li  of 
III.'  iiirn.'  H<niur.'M  into  twcnty-llv.'  miiuII  H.|iiur.''.. 
Driiw  tint  iVft  uh  in  tin-  .'opy,  iw\  .M  tli.-  linri/.-nhil 
lin.'M. 

Caud-Kxkic  isK  X\I1I. 
Quatrafoll  and  TrefoU.  -  Watarbottle  aud  MouldlnR. 
'I'll.'  Hyllul.I. ■/'«■/.  fr.'.|ii.iitly  ii'*''!  in  <l«'."«iKn,  in  fioni 
t!i.'  l-'rt'n.li,  iiii'l  ni-iiiiM  l.uf,  ii«  tlu'  Ifiu'liiT  hIiouM 
..xpliiin  to  tlu'  .liil.livn  ;  l-r  Unit  will  lulp  to  fiiM.'ii 
til.'  term  ill  tli.'ir  niin.l'*.  Tnf.'iU  (Hn"'  I'liv.-*), 
.Hi;itr.'f.)ils  (four  l.'iiv.'s).  .■iiKiui'loil^'  (liv-  Ii'iiv.'-.).  uim 
lorniM  .'oiumou  in  ii.'urly  all  «tvl.'H  of  iiioiLtii  oiim- 
meiit. 


H* 


lu; 


iKAflll-.llS'   MANI  AL. 


ViiUW  II.  (JiKifi'ffoi/  oil  a  S'/iiiin:  —  Having 
ilniwii  ii  sciiiari',  ilividc  cacli 
ipf  its  sides  into  rmii'  (■<iuiil 
pai'ts.  ( )h  till'  twi)  inner  parts, 
iisabasc,  draw  a  sinijilc  cnrvi', 
with  an  altitude  e«jiial  to  one- 
lialt'oftlie  base.  Tliese  enrves 
aro  toils ;  and,  as  there  are  tour 
of  them  in  this  instance,  we 
liave  what  is  eaUe<l  "ijuatre- 
I'oil  on  a  s(]uare." 
l-'oiiM  //.  Trefoil  0,1  a  Tm'^.v^'.  —  Draw  ai»  «'(iui- 
hitoral  triangle.  Divide  eaeli  side  into  four  I'qual 
parts.  Ontlie  two  inner  parts  of  eaeh  side,  as  a  hase, 
draw  a  simple,  curve  or  foil,  witli  an  altitude  e.|ual  to 
one-ha'f  of  the  basi . 

FouM  c.  A  WaU-r-IioHh.  —  Draw  tlie  central 
vertical  line,  and  divide  it  into  six  e<pial  parts.  Ad<l 
the  two  other  vertical  lines,  one-si.\th  of  their  length 
apart.  On  the  lower  halves  of  the  outer  lines  as  a 
base,  draw  simple  curves,  with  an  altitude  e.pial  to 
one-half  of  their  hase.  Connect  the  i.'wU  of  these 
curves  by  horizontal  lines;  add  the  bottom  aiul  the 
short  horizontal  lines  above. 

FoiiM  (/.  -/  M'lulilbxj  rompoml  of  Siiiijili-. 
Cui'i'cs.  —  Draw  two  jiarallel  horizontal  lines,  of 
anj'  lengtii,  and  of  any  given  <listance  apart.  Divide 
the  intervening  space  into  squares,  and  draw  their 
diagonals.  Where  the  diagonals  cross  each  other  will, 
of  course,  be  the  centre  of  the  square.  On  each  side 
of  each  semi-diagonal,  draw  a  simple  curve.  Add  a 
horizontal  line  above,  and  another  below. 


ri;  —  Iliiviiij; 
),  tliviilc  ciuli 
U)  t'liiir  ('(|iial 
rti>  inner  jiiirts, 
I  !<iiiiiili'  ciirvi', 
cqiuil  tt)  oiic- 
'I'liivsf  ciivvi's 
*  tliiTc  iirc  four 
s  instiUK'c,  We 
iilli'<l  "quatic- 

Diaw  ail  t'(mi- 
ito  four  ('(lUiil 
side,  as  a  Inisc, 
titiuli'  ciiual  to 

\V     tllc     ccMtrill 

al  parts.  AtM 
i»r  thi'ir  loiif^tli 
iter  lint's  as  a 
itiuU'  (Mjiial  to 

ciicls    c)t"    tllCSI! 

ottoiu  and  tlui 

•d  of  Si)iij)/i^ 
tntal  litit'.s,  of 
apart.  Divido 
iiui  draw  their 
each  other  will, 
On  each  sidt^ 
curve.     Add  a 

|\V. 


sfMi'i.i:  (I  liVls 


m 


This  inoiddinj^.  wliosc  unit  is  iIh' >anu' as  .\  in  Card- 
K.xercisc  XVI.,  ilhistrali-s  iwo  principli  s  <il' di'.^iun. — • 
Hyiniuctrii-al  arran^^enu'iil  alioul  a  (•iitri',  auij  hori- 
ZdUtal  repetition  ot'  the  unit. 

< '.vi;i>-iv\i  i.'Msi;    XIX. 

LozenKO  MouldicK. —  Siinplo  Uurvci  on  a  Square,  and 
Simplo  Uui'ves  in  iv  Square. 

Kidt.M  II.  —  I)ra\v  thi.  ,  (,r 
more  M|uan's,  united  hoii/un- 
taliy.  Draw  their diaup'ter.-. 
wlio>e  points  ot'  intersection 
will  ,i;ive  the  centres  of  the 
s(pnires.  <  )n  each  upper  aiid 
lower  >ide  of  each  sipuire,  as 
a  liase,  ilraw  a  senii-i-ircle 
throujjh  the  centre.  .Add  a 
horizontal  line  aI>ove,  and  an- 
other helow. 

Komi  //.  Srini-rirr/rs,  or  Siiiiji/n  ('in-i'i.'n,  oti,  a 
S/idnr.  —  Draw  a  sijuare  on  its  diameters.  Using 
the  lar},'er  part  of  these  diameters  as  diaj^onal.s,  draw 
an  inner  scpiarc  On  each  sidt-  of  the  inner  sipiare, 
draw  a  semi-circlo.  Erase  all  hut  the  inner  .square 
and  the  semicircles. 

l"'oitM  ('.  Siiii/ile  (Uiri'cs  in  a  S'/ikh'i: —  Draw 
a  square  and  its  diagonal.s.  ])ivid('  each  si<l(M]f  the 
square  into  three  equal  parts.  Connect  jhi'  upper 
division  of  the  loft  side  of  the  s(pnir(!  with  the  right 
division  of  the  lower  side  of  a  s(piare  hy  a  sinq)le  >'urvo 
ilrawn  through  the  centre  of  the  s(piare.  Draw  tho 
three  corresponding  curves. 


Ci.s 


Th:.\'  IIF.IIS'   MAMM- 


rour-polnted  Star,  Outline. 

l)riiw  ii  ><niiirf.  mill   tlivi'lf 


it  iiitii  iiiiii'  .si|Uiiri'>. 


On  I'lifli 


Mtlf  of  tlif  iiui.'V  s.nmiv.  ilniw 
an  isos.M'l.'s  U-v.w^h:  witli  i'"* 
iil>cv  in  tlli-  .■.■l.tlT  of  til.-  .ni- 
v.'sitondinj,'  si.lc  "f  tli-  hiV'A'' 
Kviis."  all   i'x«'''l''  '•"• 


S(iiiav<v 


sid.-liiics  of  till-  tniui-^'li'^. 


Caku-Kxi:u<  isi.  XXI. 
A.  Bird-House. 

Driiw  ii  s()Uiiiv  ;m<l  its  di- 
.^,„,.t^.,.s.  On  thi»,  us  ii  bas.'. 
.■oustruct  the  lionsi-,  without 
further  (lircctioiis.  'Ihis  is  ii 
-rood  fiUMrc  for  idass  analysis. 


.  <--,a«BB  —  BepeatinK  Form  for 
Douole  Squares  ani  C.-osses.      rveuoa 

covering  Surfaces. 
Draw  three  or  ...ore  parallel  horizontal  lines  .U;  tlu- 
sa,..e  .lista..ee  apart.    1  .raw  three  or  more  vert.eal  l.t.e  , 
c    ssins  the  ho;ix.o,..al  Ih.es.  and  forn.u.R  a  sc..es 
s^.,are'     The  whole  >late  or  l.lack^ourd  t..ay  thus  ho 


V.  iiud  tlivitlo 
,n.>,  1)11  I'lifli 
r  siiniirt'.  ilf^^v 
Illicit',  \vitli   i'^ 

tn-    nf   till-  (iil- 

ot'    till'    lill'iii' 

all    I'Xi'i'pt  tlic 


iiiv  iiiid  its  ili- 
tlii»,  as  ii  base. 
lioiisf,  without 
)iiH.  'I'liis  is  a 
•  rhiss  aiialy!*is. 


atinK  Form  for 

imtal  lines  at  Ww 
lore  vertit-al  lint'S, 
•iiiinR  a  serifs  of 
)unl  may  tlms  l)c 


SIMPLE  CI  UVK^. 


m 


.•oVfiHMl  with  s.|naivs.  I)ivi4.' .•a.h  si.l>"'f  <a.  1i  Mpiaiv 
into  two  npial  parts.  Draw  ohliquf  lim-s,  foniMctin^' 
the  iioiiiis  of  division  an.l  forming;  a  sipnirc  witliiii  .m.Ii 


of  tlio  original  .siiuart's.  Divi(h'  earli  si.l.'  of  tlic  lust 
fonnc.l  s.|iiaivs  into  tluvi-  .■(iiial  |  arts,  aii-i.  tlirou.!.'h 
till'  points  of  tUvision.  draw  liiu's  paiali.l  with  tho 
sid.'s  of  tlic  oiiMinal  s.piarcs.  and  fi.rinini,'  a  third 
M.i'i.'s  of  s.piarcs.  Kras.'  all  the  lines  of  the  ori-inal 
wjuares.  and  tiie  eentral  tliird  of  .-aeh  sid.-  of  tin'  la-t 
s.pnires.  There  will  he  lilt  a  ic^'ular  s.ri.s  of 
di>\ihli'  sipiares  and  irosscs. 

The  same  vesnlt  nniy  he  ivaehi'cl  in  tliis  way.  avoid- 
m-^  the  lirst  series  of  stpnirfs.  Draw  a  sipnire.  or  an 
ohluii^'.  of  deihiite  size:  an  ol.lon-.  for  rxaiiiple.  fonr 
in.'hes  hy  six.  Divith' the  sides  into  .Mpnd  parts,  an 
ineh  or  two  inches  Ion?,  for  in-tanec  l!ci.'innin,i,' 
with  the  points  of  division  neaiv-t  tlic  corners,  con- 
nect all  thf  points  hy  ohlicpic  Inics.  lorniin.u'  a  scries 
of  ohrKpn"  s(pnircs.     Finish  as  in  the  lirst  mode. 

Dire.'t  the  attention  of  pupils  to  similar  forms  to 
he  found  in  cari)et:i,  wall  papers,  &c. 


ro 


■ILMUIKlis'    St  A  SUM,. 


Ueml-oiroloB  and  BtnilRht  Lines  for  oovorlns  HurrucoR. 

I'iMU  :i  x'rics  (irsi|ii;»ri's 
t(»  111)  tln'  sl;it('  or  Idai'li- 
liDiinl.  IHviilc  ciii'Ii  niili' 
(>r  I'iicli  siinarr  into  I'lmr 
.(jUiil  ii.irts.  Oil  till'  two 
iciitiiil  imrts .  of  fiicli 
si(l'.  ilriivv  II  scnii-i'irt'lc, 
tcisilin^  iiltiTii.itrly  li>- 
j£  wiinU  iiiiil  tVoiii  tlif  niitri' 

of  till'  scjuari". 

('AI!I»-KxKIII  MI".    XXII. 
Forms  for  Bopotltion,  composed  of  Simple  Curves. 

KoiiM  ('.  —  l>ri\\v  two  pur- 
iillrl  lii,ii/i>iital  lines  of  any 
Icnj^lli,  ami  at  any  Kivcn  dis- 
tant-.'apart.  Diviili'  thi'spaco 
lu'twi't'ii  tlii'iii  into  s(pian's. 
Diaw  till'  ilia<,'oiials  of  tlio 
s(piari's,  and  divide  I'lvcli 
.scmi-dia^'onal  into  two  fcjual 
parts.     Conncot  tlio  opposito 

oiids    of    caib    diaj^onal    l-y 

simple  curvi'.s  drawn  tlirough  tin-  divi.-ions  of  tlio 
otlur  diagonal  of  tlic  same  square.  Add  a  horizontal 
line  aliove,  and  another  Ix  low. 

Yoixsi  /,._r)niw  a  series  of  squares,  united  horizon- 
tally, as  in  A.  Draw  their  diameters  and  diagonals. 
Conneet  the  ends  of  the  horizontiil  diameters  to  tho 
*'ii(ls  of  the  vertical  diameters  by  seini-eircles  drawn 
thiou:Ji  theeentresnf  the  squares.  TaUiiigeaeh  half  of 
the  vertical  lines  which  se^iarate  the  sipiares  as  ft  base, 


\ 


oriDB  HurracoR. 

x'rics  (if  si|ii;»ri'H 
shiH'  III'  liliii-l\- 
'iviilc  ciu'li  Hiilt' 
(inarr  iiiti»  lour 
[s.  Oil  till'  two 
liirts  of  oacli 
V  a  scmi-i'irclt', 
iiltiTii.iti'ly     I"- 

I  t'ri)in  the  niitii- 

I. 

Iniple  Curvei. 
- 1  >iiiw  t\V(»  psir- 
al  liiu'.t  t'C  any 
t  any  j^'ivcn  dis- 
Diviili'  till'  .HpacH 

II  iiitii  si|iiaii's. 
iajiKiials  of  tlio 
I  (liviilo  oarli 
1  into  two  (Mjiial 
oct  tlio  opposito 
•h  i\\i\^o\ui\  \>y 
ilivi>ioiif".  of  tint 
AiM  a  liorizonlal 

,,  united  liorizon- 
<  and  diayonids. 
(liamcterd  to  tho 
mi-i'irclcs  drawn 
Uiiigcaidi  half  i)f 
ipiari's  a.s  a  buso, 


>/.»//•/./•;  rr/.'fA.v,  t* 

draw  1.11  raidi  mdf  of  tlii'l-aM'  ^iinp!.'  iurv<-<.  to  iinlto 
Willi  till'  s.'ini-cirrli-v     Add   a   liori/mital  linr  aLov. 

and  aiiotlnr  Im-1'>w. 

I.',,, .J,  ,..  _  Dniw  ii  scrii'S  of  Miuaivs.  a>  in  lln'  last 
two  ••xcri'isi's.  Draw  lliiir  diami'li'i>.  <  >ii  carli  side 
of  ca.di  .Hqiiarc,  as  a  l.asr,  draw  a  -.iiii-ciirli-  tlimn^di 
tlic  I'Liitiv  of  the  siinaiv.  Tlim  draw  a  einle.  pa»mj; 
till i^h  the  ends  of  the  diameters. 

As  an  addition  to  these  exenises.  draw  a  similar 
M-riis  of  sipiares  ahove.  and  another  l.elow.  eaeh  nnilid 
with  the  lirst  series.  Till  these  sipiaivs.  in  the  .same 
manner  as  the  lirst  were  lilled.  with  mrves.  If 
they  are  correetly  drawn,  they  will  in  liuli  ease  form 
an  involved  s.'ries  of  i^erfeet  eirele.s.  ( )iiiit  the  paral- 
lel horizontal  lines. 

These  exercises  for  eoveriiiK  a  surface  will  be  found 
^r„od  ones  for  the  pupils  to  practise  fre(|neiitly. 
Much  of  what  has  been  learned  in  previous  lessons 
will  be  brought  into  use.  The  pupils  should  be  jki- 
mittod  to  cover  their  slates  with  su.di  forms,  and  also  to 
draw  them  with  many  repetitions  on  the  blackboard. 
If  a  slate  is  tilled  with  them  carefully,  tb.re  oiij,'ht  to 
be  considerable  improvement  between  tiie  iii>t  and 
the  last  linos  drawn. 


(iuKSTiONS.  —  Dcscrik-  a  curve.  A  simple  curve.  A  «iiiail- 
rmit.  A  semi-circle.  What  are  the  tVaturcs  i.f  a  circle  >  What 
is  the  base  of  a  curve?  The  altitmie  ?  Wh:>t  i>  n  chonl  ?  An 
arc  '  What  is  the  .liirevenee  hetween  the  iiiatheinatical  aii.l  tho 
iK.piilar  use  of  the  word  "circle"  ?  How  shimM  .letiiations  ho 
^.iveii  to  chil.lrcin  What  of  the  wor,l  "  ruun.l  "  '  AVhcii  is  a 
eiiele  said  to  he  circumscrihed  ahoiU  a  .-quaiv  7  Inscriheil  in  a 
M,aare  ?    What  is  meant  hy  "  foil  "  >■     Trefoil  ^     U.uuieto'.l  < 


CHAI'TKi:    IV. 
( ..Mi'di  Nil  (  Tuvr.s -Tin;  kllii'sk  and  oval. 

Tins  ruvwc  liMvc'cliMit  ultli  siini-lfciirvi's;  tliiit  is. 

Willi  .'iii'vi's  struck  Ib^iii  one  n.iitiv.  iiml  liiiviii^-,  I'on- 

sr.|iic.|itly.  tl.csiimi'  ilr;,Mvc  ,.f  ciirvatmv  in  ov.-ry  part. 

All  s!iii|ilc  .'urvi's  arc  par^-  "f  circles,  iiiid,  if  cniitiii- 

ucil  tar  cii  .'i^'li.  Iicioiuf  circles.      A  circle,  therefore, 

is  1)1  t  ail  elKliess  siinjile  curve.      A  coliipnllll<l  curve  is 

a  curve  lliiit  does  not  l>en<l  ref,Milarly  tliroiiylioiil   its 

wlioie  len;,'tli.  ainl  must,  therefore,  lie  struck  fiom  two 

,,r  more  centres.     .Vs  the  curv(^   is  ilriiwii,  the  de^'ree 

of  curvature  uiay  chaii^;e  at  every  point,  us  iit   the 

.■Ijilise;  or  it  may  chan^'e  at  intervals,  as  in  the  oval: 

while    it  may  completely  reverse  its  direction,  as  in 

the  ocec. 

Tho  Ellipse. 

Thi   r//lj>sr  is  II   jihllir    fh/lirr   /loiniifrif 

III/  a  ('itiii/iiiiniit  riirrr  sfriir/:  froiii    firn 

rnifrfs  (A). 

There   are  many  curious  things   to  l.e 

said  ahout  the  ellipse,      [t   is  the   f.u-m  a 

circle  appears  to  tidie   when  viewed  ol.- 

and  a  circle   is  always  viewed  thus,  except 

when  til!)  eye  is  directly  opposite  its  centre.     Draw 

a    circle    on    the    l.hudd.oard :     step    to    one    aide 

and   view    it,    and   the    circle    will    apparently   l.e- 

.•ouie    an    ellipse.     Draw  a  circl i    a   .slate  :    turn 

the    slate    from    tho    eye,    and    view   the    .-ircle  :    it 


;   AND  OVAL. 

Lirvt'H;  tlint  in, 
I  liiivin^',  fnii- 
iii  ovcry  part, 
md,  if  foiitin- 
rolc,  thcrcfort', 
|inuiiil  I'lirvi'  i>* 
liroiiyliiiiil  its 
nidi  fi.iin  tWH 

rt'll,  till'  (ll'f,'Vf(' 

iiit,  us  ill  tln' 
[IS  in  tlu'  "Viil : 
lirection,  us  in 


tii/iifc  hninxlril. 
in:/:  from    tn-n 

s   tliinfjs   to  I'c 

is  tin'   t'linn  u 

icn  vi('\vi'il  <>1>- 

(1    tllllS,    CXCt'llt 

centre.     Druw 

to    one    sitlo 

iiDDarcntly    1»'- 

u  .sluli' :  tnrn 
thf    circlf  :    it 


ro.i//'or,v/>  <:rt{yh:s.  *■> 

will  liirn  tali.i  tin-  form  <>!'  un  .11  ipso.  Hold  ;i 
lio..p  in  u  vi'itii'ul  position,  wii'i  its  cMitro  diri'.'tly 
in  front  of  tin'  vyr  :  \\u-  Imop  will  then  1m.  scimi  as  u 
rinlc,  — its  ri'id  foini.  Tnrn  tin-  lioop  from  tin'  "•ye, 
iind  its  form  will  m.priir  to  Imv.'  .■Iiun'_'id  t'.  lliat  of  :in 

cliipsc.     Tin'  farther  tlir  I p  is  tnrned  tVoni  tiie  eye. 

the  liutter  will  heeoine  tiie  ellipse,  until  its  two  sides 
nn'r!,'e  in  one,  iind  only  a  strai),dil  line  is  se.^n.  TaUi' 
u  round  stiek  :  ent  it  uim-oss.  ol.li.pn'ly  and  e\enl.\  :  ilie 
shape  of  tlio  section  or  scurf  will  l.e  that  of  an  .'llip^e. 
The  more  ol.li.pn-ly  tin'  sti.'k  is  ent.  the  ^nater  will 
hi'  tin'  length  of  the  section  compared  with  its  l.nadth  ; 
hut  it  will  always  l.e  an  ellipse. 

A  disk  or  cone  atVords  the  hest  means  for  illnstriit- 
in;;  the  ellipse;  hut.  if  the  jiroper  models  nre  want  in;,', 
th.'  teacher  can.  hy  usins  the   moiles   ,,f  illu>trati..n 

just  described,  familiarize  the  pupils  with  the  »  \Uit 
'form  of  the  (dlipse.     It   is  essential  that  they  sln.nld 

he.-ome  perfectly  familiar  with  this  curve,  w   it   is  so 

freipii'iitly     einph.yed     hy 

hotli  artists  and  artisans, 
'i'o  draw  a  coin',  with  an 

ohIi(|Ue   view  of    its    base. 

lii>t  draw   an  ellijise,  and 

then   add    a    vertical    and 

twoohliijue  liin's.  as  shown 

at    1'..     The   ohli.pie  lines 

hIiouM    not    be   drawn    to 

tin'  ends  of  the  Iotijj  diame- 
ter,   but     tanj,'ent     to    tlie  _ 

eiirve.      l'>e    particidar   to  ^■ 

observe    this.     Erase    the   diameters.     Draw   several 


74 


7>.ir»A7,-.s'    W  I  V/',0, 


cimi'H,  \i\v'mg  a  in«irf  or  h'**  i>\<\'u\\u'  vii'w  <>f  Mio  t)!iM.. 
llUi^tniti-  witli  II  iiiiHlt'l. 

Tilt  !••■  ail'  iiiaiiv  \;nialioii^  in  tin-  f'lnii  i»f  tlii'  flli|>'<'. 
Hiiirc  il.H  r<iiiii  tli'iH'M'U  oil  till' .lilViTi'iiif  Itftwcfii  it* 
IniHtli  iintl  it'*  l-ri'iultli.  It  may  In-  M.l.rou.l  ii*  .IomI.v 
f..  apiiroiifli  a  riivl,..  or  ^n  iiiirrow  ii^  to  apiirnu.li 
.•loM-ly  11  Mnii^'lit  I'mi-:  l-iit.  wliiitcv.T  it?*  foriii.  it 
al\viiy«  rttaiiis  fi-rtiiiii  tliotiiii-tivt'  fi-iitiirfx. 

Itolli  its  Ion;;,  or  fr'tiisrirsr  .liiiinctir.  iiml  its  nliort, 
or  ,,„ijii<rih-  .liaiiict.'r.  .lividc  tin-  .'Ilipsc  into  two 
HiniTliir  i'liuiil  parts.  Tin-  two  (liiiinoti'rs,  l.iHwtiuK 
I'lU'li  otlior  at  rij;ht  an«l''.S  'livitlf  tin-  .Hip-*.,  into  four 
niniilar  cipial  parts. 

If  it  is  rcipiiri'.l  t<>  flml  tlif  two  centres  of  an  el- 
lipsc   iilnii  ly  ilniwn,  tlien   draw  fronj    an  end  of  tin- 

sliort  iliami'ter  two  ol)li(pie  lines,  on i  eilher  sid". 

to  the  lon,^'  diameter;  eaeli  o»'  tlii'sr  ..hli.pie  lines 
lmvin«  ii  lei.jjth  eipial  to  one-lialf  of  tin-  lonjj  diiinn- 
ter.  Where  the  oldiipie  lines  toiu-li  the  ionj,'  diani-- 
ter  will  1m;  the  two  centres,  or  Jjrl,  of  the  ellipse. 
N(.w  take  any  point  in  the  circumferenee  of  the  el- 
lipse, and  draw  a  line  iVom  tliat  point  to  each  enntro 
of  the  ellipse:  and  these  two  linos  iinitod  will  e(pial 
the  length  of  the  Ion},'  diunieter.  If  that  .liaineler 
is  two  feet,  for  exaniph',  the  two  lines  will  meaHurf 
two  feet.  If  these  two  oblique  lines  do  not  eipnd 
the  len^'th  of  the  lont,'  diameter,  then  it  follows  that 
the  ellipse  is  not  i-orreelly  drawn. 

liarge  ellipses,  of  dilVerent  proi>ortionH,  should  he 
drawn  on  the  blackhoard.  from  time  to  time,  f..r  the 
pupils  to  study.  This  can  be  easily  <lone.  Take  a 
pieoo  of  thread;   tie  a  loop  at  caeh  end;   stick  two 


s 


\'\\  of  Mil'  tia><f. 

II  111'  till'  t'lli|fi'. 
m-c  bi'fwi'tii  ill 
liritiul  ii->  rliiM'ly 
lis  to  a|iiir<>iirli 
•IT  its  I'lirni.  it 
irt'H. 

■r,  ami  its  Hlmrf, 
lli|isi>  into  two 
U'tiTH,  liiset'tiiiK 
I'llipHc  into  four 

iciitrt'H  of  ail  I'l- 
aii  I'liil  of  tin- 
on  I'itlii'i-  sill". 
i>  oi)lii|iii'  liiH's 
tin*  h>ufi  iliiinn- 
tlii'  ioii^  iliann- 
,  of  tlio  I'liipst'. 
trt'nrn  of  till'  I'l- 
it  to  encli  o«ntro 
initpil  will  t'linal 
f  tliat  iliaini'li-r 
I's  will  nu-asuii- 
L's  do  not  *-i|nal 
n  it  follows  tliut 

■tions,  nlionlil  l>i' 

to  tinii",  for  tin- 

y  iliiiic.      Take   a 

I'liil ;   stick  two 


voMi>ni:sn  vvii  vkh. 


W 


\ 


j»Ins  into  ttii-  MarKlioanl.  lU  a  Ii-ss  ilixtaiiii  a|.ait  limn 
tin-  li'n','tli  ul  till'  lliriM^l;  pnl  a  liin].  o\.  r  .a.  Ii  |.iii. 
wlii'ii  tli«'  tiiirail  will  liuiiK  loo^ily;  |»i'f.Hs  a  rva.von 
u;,'aiuHt  tilt'  tliri'ail  until  it  i"  ivmli  ri'l  tani  ;  t'nii 
fanv  tin  cravon  ai'oiiinl,  toiiiliiiiK'  tin-  lihu'klioaril.  aii'l 
niakinj,'  an  i-Ilipsr. 

If  an  illipsi'  is  iii|uiri'il  liavinj;  iliann't/i'rs  of  ilrii- 
iiilr  li'iif^tli,  as  a  Ion;,'  iliain.'tiT  of  tliiri-  fi'it  ainl 
II  .-liort  tliiiini'tiT  of  two  flit,  iliaw  tin'  iliannlii', 
iinil  linil  tin'  iiiitri's  of  tin-  illips...  as  uln-inly 
ilcsfiMlifil.  I'liu'iuji  an  <'n»l  of  tlir  tlif.ail  at  larli 
of  thi'sc  ci'iitii's.  witli  slark  i'iioiij,'li  to  allow  tin- 
cravon,  wlifii  pri'ssi'i]  a;,'ainst  tin-  tliri'ail.  to  touch  an 
ciiii  of  tin-  nliort  (lianii'tiT,  draw  tin'  flli|isi'.  wlicn  its 
lioiindary-litn)  will  pass  tliroiiv'li  tlif  ••mis  of  l.olli 
diaini'liTs.  ami  lie  of  tlic  n'i|niri'd  proportions. 

|{y  diawinj,'  tin-  cUipsf  in  tliis  nninmr.  tin'  cliildnn 
will  nnvlily  puncivt?  wlnvt  is  nicunt  wln-n  it  is  «aiil, 
that  tliii  fUipsi'  is  a  coinponnd  riirvi',  struck  from  two 
cciitri's.  As  the  two  [lins,  or  two  centres,  are  brought 
nearer  and  neiuvr  together,  tlioy  will  readily  perceive 
that  the  ellipse  approaches  nearer  and  nearer  a  circle, 
while  it  never  becomes  a  circle  until  the  two  loops  are 
placed  over  onu  pin  and  the  curve  is  struck  from  one 
centre.     Literally  no  figuro  can  have  two  centres. 

Children  need  not  be  taught  all  that  is  here  said 
about  the  ellipse  before  they  begin  to  draw  it.  Indeed, 
it  is  best  for  them  to  acipiire  a  knowledge  of  its  fea- 
tures along  with  their  drawing,  and  so  acquire  that 
knowledge  gradually.  They  should,  however,  have  a 
di.stimt  idea  of  the  form  of  an  ellijtse  before  thoy 
begin  to  draw  one  freehand.     This  they  can  obtain  by 


7»l 


THAVUkHs'    W.I.Vf  .W. 


vhvvlug;  n  <ir«'l.'  i.l.li<|i«<ly,  hy  vi.'wtt»«  tin  m-tnsil 
i.lli|,,...  .  itli.r  .Imwn  nii  tit.-  Iiouid  or  -lu.wii  »•>•  i» 
111.1.1.1.  Ill  .itli.  !•  "I  111''  III"!  tw..  .ii-.'K.  til.-  .'.v.-  iiiiiHt 
Im'  tliri-.-rl.v  ..|.|M.'it.-  ll;-  tnu-  vinxtrv,  or  iM.iiit  wli.  r.- 
tliM  twu  iliiHwt.'f*  iiitt'r»'«-<'t. 

'r.i  .Iniw  mi  i-llipi..'  IVi-i-liaii.l.  i»».  «f  A.  1m  «iii  l.y 
(IruwiiiK  IV  v.-rti.iil  liii«'  l'.>r  tlu"  truu^v.-r**-.  »r  I..11K 
(li.im.-t.T.     Divi.l.'    thU   liii«'    !•»»•>  »^v.»  .-.iiml    |.iirt-<  i 

tlll'nll;{h    til.'    lioitlt   .if  «livi«i.>ll.  .Imw   ;l  l|..li/.nllllll    lilL' 

foi- til.-  xli'.rt  iliiim.-t.-r,  Imviiiy  "ii.'-lialf  tin-  l.-tiKtli  ..t' 
till-  Icii^  ili.iiiu-t.-r.  Tliv..unli  til-  i'IhU  of  thm-  .liiim- 
i.ti-rn.  .Imw  til.'  lM,iiii.li(iy-liii.'  of  tli.;  .llipsf.  S.-.-  tliat 
IH  iiurt  <.f  tins  lM.u!,.l.in-lii>o  \*  Hlr.UKl''  !  ♦*•■'*  '•  ""- 
\vh.-iv  iiiiiU."  u  "liiup  til -i,  ;  tliiit  .-lull  .|iiiirt.i  »(  tlxi 
..lli|wliii.«  tlii'HimH'Hlia|..-  Ill  th.-  otlx-r  tlii-t-c-.|iuui.rH. 
ll.-.iuiv.,'  tlh-  pupiU  t.)  .Iniw  til-  ^iinii-  oil  flu-ir  nliit.-, 
iiiiikiiiK  till-  loiiK'  iliiiiiu-t.-r  f..iir  incl.t'S  for  i-xiiiiii>l.-, 
aii.l  till*  sliort  .liaiiH'ttT  t\v.)  in.  hex. 

After  Bevt  rtil  «-nii)»('«,  with 

til.'  j)ro|n>rtioii»<  1  X  -  (<"'•'  ''.V 

\\M>),  lik.'  III.'  "in'  »t  A,  liiivo 

1h-(-ii  tliiiwii.  thi-ii  iliiuv  iitlii-ix, 

with  tlilVi-n-iit  )ii'nii(iitii)iis.  iiiiil 

ill  .lilV.T.iil    lM).Hiti..iii»,  UK  at  ('. 

It.-.iuin-   tho  pupili*  t.i  r.pr..- 

.lucc  thi-m  on  their  xhit.--*. 

Tilt'  piilh  of  th.-  t'iu-th  iihoiit 

thi- sun  is  nil  .'llii-.     Th.-  SUM  i^  in  <•>..•  -f  ;♦«  »";'l 

l,„t.  w.-r.'  an  .Uil's.'  drawn  ..n  th.'  hla.khoar.1  1uivm.« 

tho  sam.-  pr..porti.Mis  ns  th.'  ..rhit  of  th.-  .-avth.  it  wonl.l 

1m  .  p.-rhai>-..  inip..ssil.h<  for  th.-  unaidcl  cyo  to  ti-ll   it 

from  a  triu-  .'in-le. 


r»j(    till    iiftiiiil      I 

till-  I  yi'  iniiMt 
»r  |M)iMt  wlit'i't' 

t   A.  Ill  i^iii  l>y 

VIT*I',    "t    llltl(( 

i'(|iml  |i:ii'l-* ; 
liiii'i/iiiitiil  line 
'  tlif  ItriKtli  <il' 
(if  tlx'Hf  iliiun- 
ijmt'.  Sci'  tliat 
lit  i  tli;it  it  iHi- 
Hiliirtc  r  'if  tliii 
tliriy-niuuttrM. 
nil  tlii'ir  Hliitfi*, 
*,  t'lir  cximiiilt', 

I  cllipf't'M,  with 

I  X  -  (<"'♦'  h' 
out'  at  A,  Iiiivc 
in  (Iriiw  iilliiTK, 
iriilmrtiuii"!.  mill 
.sitiiius,  as  at  ('. 
Miiiiln   to  niirii- 
lifir  xlatt'i*. 
till'  t'lirtli  iilii'iit 
i,iii>  lit'  itH  ftu'i; 
iiklMiiinl  liuvhiK 
cciiitlt,  it  wi.iiM 
III  eyo  to  tfll   it 


T7 

iiil.l 


vtnii'nrst*  i:i  uvas. 
An-  AuTixr't   I'MKrif;,  —  l»ii»w  uii  <Hi|»''< 

ttir     IllUulli'     lHltl     llllllllii-lltlli'         I'll'' 

iiiiii'kM  on   tin-    |»i»li-tt«   »»1>"W  wliiM'f 
t)it>  rtilor  i"  iioiiitlly  |iliti-i'«l. 

A  .■.lilii'iiliil  I'aiiiti'C  w;m  oiiff 
(ixkiil  Willi  wit  I'  III-  iiiixi'l  I'i"  lolor-'. 
••  Witli     liniiiiN    fir,"    lt<     ii|ili<il 

III, I I,     witlioiit     liruiii".     wirlKHil 

tliougiit,  nothing  iim  I'l'  vvull  doui'. 

Tb«  Ovftl. 
Tlif^  otfti/  In  a  fihnir  Jhfiiri  limntiliil  /*// 
,1  ,<,,iii>iiini<l  I  iirrv  •ml;/  our  of  ir/imo  ili- 

illtilfll'H  eitlHMI-H    flu-    uthvi'  at    tfll)    I'riltrr. 

Ihuw  ft  viTtii'ui   liiH-:   iliviiln    it   into 

tlim«  I'tiuui   jmrts;    tliioiiuli   liif  iij.|M'r  

iioint  ot'  ilivi-loii,  ilriiw  ii  lioi-i/oiitiil  liiii>.  D. 

UH  lit  I).  <M|mil  to  two-tliinlM  of  tin-  vi-itiiul  lim-.  Om- 
liiilf  of  till'  li..i'i/oiit:il  liiM'  I'xlinds  on  litlitT  sidi-  of  tlio 
vcrtiial  liiir.  *>ii  •'"•  liori/.oiiiiil  lim-.  Uf  ii  I'usf,  <liuw  a 
Hfini-riri'lt'  tliroiijjli  tin-  n|ijii'i-  i'ih!  of  tlir  viTtiiul  liiif. 
On  flu-  lowtT  two-tliii-il-'  "f  tiii'vciticiil  liiii'.  drawoiii'- 
liiilf  of  111!  I'llijif"',  to  iiiuii"  witli  till'  ends  of  llu!  M'lni- 
c-iirl.-.  TIiiH  ii'wvn  im  "Vid,  or  «'K'«-Hliiiiicd  IlKurt'.  iix 
tin-  word  nifJiiiH.  oii»>  imrt  of  wliosc  iMtniiiliiiy-liii" 
is  u  !.ini|ili'  cuiv.',  tlif  otlii'i-  piirf  an  "Uipxc 

It  will  Iw  HiTii  that  thf  lon«  diaiiK't.T  dividi-n  tho 
oval  into  two  Pfiuiil  .similar  imrts,  and  that  tin-  »<liort 
diami'tiT  ihyvn  mt  W«  nay  two  i->jiiof  >i!iiiil>n' 
l>arts.  "  Eijnal  "  n-fiTw  to  the  arcu,  or  Hurfacf ; 
"simihir"*  nl'i-rs  to  thf  slmiH'.  Hi-nco  two  <'(|iial 
figur«'»  may  have  diiVcivnt  hIiuih-s;  whilf  two  similar 


V 


-J 


fi 


tflWHUUM'  MASirAL 


Muutf*  miiy  lukV"'  ilirt'iTfiit  unnw.  A«  tin*  two  |»iirti« 
v\'  llif  oviil,  nli'ii  .liviili.l  \<y  it«  l.ttii;  ilimiii'ttr, 
*lioiil>l  I"'  aliki'  ill  ImiIIi  ri'>«|M'i  ti4,  it  i«  lun  "ury  to 
«|i'M.'nlM>  tlii'iii  II*  njiiikl  similar  jiiirf *.  Kitlu-r  iliiiiiit'tt'r 
•»!'  uii  I'lliiiM',  Nvliifli  U  xonit'tiiiuH  I'ullfil  lui  iiviil,  l»iit 
|.  hot  itit  oViil.  .livi.li'-t  it  \u\i>  two  i.|iml  MJiniiar  piirtit. 

It    IM  not  fuMUnliul  to  UII  oMll   lllUt    III*  ImHIImIiU>-I.II«» 

Ih'  ill  |>iirt  a  •Inlf,  iukI  mi  «lliii«'  in  purt.  lik"  !'■ 
On  tlif  otliiT  liiiiiil,  it  limy  !»•  <oiii|io-.f.l  wlioily  o|^ 
|iiHtH  ofilitVcniit  iinli's  or  wholly  ol'  (nirlH  olMitVi-ivm 
(•|li|Mi'«;  or  it  limy  liiiv.- no  purt  of  u.iri'li'oriiiM'llil»«<-, 
liiit  !«'  roiniMwtM!  wholly  ol'  .ither  vutvvn.  It  i»  only 
f.Mi'iifiikl  ilmt  it  rt'tiiiii  til.'  xlmji.'  of  mi  <•«« ;  ilmt  ilic 
lonu  iluiiiii'tiT  ilivitli'  it  into  two  r.|iml  -iiiiiliir  |iiiit-. 
whilt'  tin-  "liort  (limiH'ttT  tltMrn  not.  Dmw  on  (li-- 
hluikliomd  vmimi-*  (lilVfrcntly  proportioniil  oval.,  un.i 
ri<|iiiri'  till-  piiiiilM  to  ilniw  tlicni  on  tlifir  ^<lutlM.  Do 
not  .'xpi'it  iliiit  ili.y  will  lit  IliM  -liiiw  tlicni  with  uny 
Hr.'iit  .|i'«ri'i»  of  ueiunu-y:  ho  siitimlkMl  if  thuy  gft  tlin 
);i'iM'i'iil  iili'ii. 

My  tluH  tiiiii'  till-  pupil-  -lioulil  httvi' u  ih'iir  i-oiiipit- 
hi-iiMion  of  till-  I'iivl.-,  tim  ilUpHi-,  ami  tli.'  ovul.  th...-.n 
thri'i'  iiiipojtmit  ciirvi'-llmireH.  Thfy  hIiouM  1m'  ahli* 
to  (U's<'iilu'  tin'  It'iiturcH  of  liich  Hcpamti-ly,  ami  toi-oii- 
tnist  out"  with  iinolluT.  Do  not,  howcviT,  'Irofi  tin' 
lljlui't'H  ht'H' :  revert  to  thi-m  freqiKiitly  hy  w;iy  nf 
ri'vii'W,  WluMi  IH'W  linnrcs  contiiiiiinKtiirvcs  an- to 
lie  (Iniwii,  ri'tpiiic  till'  piipiN  to  (•xainiiic  tlicni  curv- 
liilly,  to  M'i-  what  inrvf<  "'iitt-r  into  thi-ir  .•oniposition. 
(.'lartH-analyHi^  of  ii«iirt's  lulaptcd  to  tin-  piirpcmo 
hIi.miI.I  frot|Ui'ntly  inclmlo  ti  m'uvrn\  n-vii-w  of  tlicso 
curvt'H. 


I 


till'  hvit  iMiriM 
ifii^  tiitiiiii'ti'ri 
«  iii'crni'ary  to 
litliiT  iliuiiM'ti'r 

•  I    lUI  DVul.  I>llt 

I  HJiniiiir  [uxtin, 

liiiiiiMlaiy-l'iirt 

I  |iurt,  liki>  t>. 

iiMi'il  ftliolly  iii^ 

irNot'ilitVi'ii  lit 

'li'iiruii  t'llipMc, 

rvit.     It  i*  only 

■'UK  i  iliitl  iiii* 

,1  Kiiiiilur  |iiiil'<, 

I>ia\v  "11   til'- 

tlli'il   ovuIm,  Utiil 

lir  wlutiM,      Do 

tliciii  with  liny 

if  tlii'y  gft  tlid 

n  ilciir  foiiipn- 

tllM  OVttI,  tllD.ilt 

hIioiiIiI  III'  iilili' 
;fly,  iiU'l  toroii- 
vovcr,  'lroj»  tin* 
itly  by  wiiy  "f 
1)^  ciirvcjt  art'  tit 
nine*  tlii'iii  ciirv- 
I'ir  ('(iinpoMitiiin. 
to  till'  piir|M(Hii 
rt'viow  of  tlii'so 


I 


T0 


i»     info    f«.i 


VUMI'OL'Mt  UUHVl." 

Millal. 

Pmw    u   viTtii'iil    liiM',  uihI    i|ivi<l> 
.'<|itil    |iurtH.     On    lli>'    ii|i|H'r    Imll 
ilr<iw   iIm'    Ih'imI    "f   till'  niiilli't  }   on 

till'     lo»ri*r    llltlf.     tilt'     llillltili'.        Til' 
^ri'Uti-Mt     MItltll    o|     till'    lli'llil    in    Olh 

liiklf  ^ffulir  tliiiii  it'*  lii'iMlit.  1 1 
will  Ix'  M'*'ii  tliui  till'  I'lii'VfH  foriii- 
111^  lilt'  itiiU'it  of  tilt'  Im'imI  itr*>  roue 
|Miiihi|,  likf  |>iirti»  of  u:i  uviil. 


CAIiU-KxKUCrHK    XXI  i  I. 
Uouf'UlM*.  KlU,  Top. 

An    II«>l'K-<Ji..\(«^.  —  Draw   thn    r(>iitrul    vfiti.ul 

line,  uikI    li'iilt'  it  into  tlii'i'>' 

I'ljiiiil   I'lirtt.     Draw  the  lioii- 
1    fi'iif.il  liiifM,  uimI  titt-ri  tl.o  nidi' 

I  >u'«,  iiiiikiiiK  ill'"  width  of  tin- 

;;liiKM  i'(|iiul  to  iinc-tliint  of  itt 

height.    'I'Im'  tliickni>>H  of  tin* 

fruiit«    i>t   )H|iiitl    to   otic-Hixtli 

r!    tlu'    wtiltli    of    till'    ^liiHi« ; 

whili>  tiio  top  uii<l  liottuiii  pro- 
ject from  tliu  ^likMri  oiht'^tliinl 

of   itH  width    within  the   oliioiig   fruiiiu.     Dniw  tho 

coinpouml  eiirvex,  extentliiiji  ♦Nvo-thinli*  of  the  leiij^tli 
I  of  the  friinie,  iiiitl  niiikin^  the  wiiint  of  the  ^Iumh  e<pial 
I     to  one-third  of  itH  grcutvHt  width. 

A   KiTK.  —  Driiw  the  central    vcrtieal   line  of  any 
givi'ii  length,  and  divide  it  into  three  e<|iia1   parts. 


80 


TE.U:lll-:US'    MAM'M- 


Thran^l.  tlu.  u,.,...r  ,.oi,.t  of  .livi.iou,  .ln.w  a  lu.n/on- 
tal  liiM- two-tlm-.l.s  UH  Ion-  as  iW  v.rtu.il  Ii.m;.  Om 
this  l,.,n/o,.tal  liu..,  as  a  l>as.-,  .Iraw  a  .<■....-.■..■.•.• 
t,,,..„,,l,   ,1...   toi,   «!■  tlK  v..rtieani,.u..     Hum  j-mnts 

,„,,,    ,1 n.ls   of  tlH-  l.ovi/.ontal  lin.s  .Inuv  o  ...,.1. 

,|,„.s    totlM.   l.ott..n.   of  tlu.   v.rti.al    line.     A.M    tlu- 

l,,,iut  at   tlH.   to,.,  au.l  th.  sligl.t  cams  at  th-  npi-r 

ends  of  till'  ol>li<iiif  lines. 

A  T<.i..- Having  .Iravvn  a  vertical  lim-  of  any 
given  len«t!,  .livi.le  il  into  three  equal  luuts^ 
Thron«h  th..  ni.l.er  ,.oint  of  .livision,  .Ir.aw  a  horizontal 
li,..,  ,,„altotwo-thinlsofthevevtiean.ne  D.vule 
the  loL.rthira  of  the  vertiealline  into  haves  ami, 
thro.iKh  the  iu.int  of  division,  .Iraw  a  very  short  hori- 
zontal line.     ('onne.:t  the  en.lsof  the  hur,.onta  l.nes 

1     „.  .itlH-r  .si.le,  by  an  oblique  line,  forming  the  stra.^ bt 
sides  of  the   top.     Draw  the  bcri.ontal  l.nes  a    the 
„j,  ,„,Uin.  the  upper  one  son,ewbat  les.  tban  atlnn 
..fth.vert.eal  line.     A.U  the  curves,  the  remamiag 

!     horizontal  lines,  and  the  peg  at  the  bottom. 

Acorn  and  Cup. -Ovoid  Form. 

Draw  a  vertical  line,  and  divi<le 
it  into  three.. lual  parts.  Throu.ub 
the  lower  division,  draw  the  long.-st 
horizontal  line,  equal  to  two-thir.ls 
of  the  vertical  line.  Upon  this 
^k.'leton  construct  the  fignve.  The 
oup  i8  a   semi-circle ;   the   acorn    a 

^__^^_^  semi-ellipse ;  the  whole  is  an  oval. 

Add  the  stalk  at  the  bottom. 


WW^^^WM 


r^ 


(lv:uv  ii  liiiri/on- 
•rtifiil  liiii'.  «>» 
[vw  ii  scnii-i'iifli' 
I'.  Krniu  Jioiiits 
111',  (Inuv  olvliiiiu' 

line-.  A«M  tli«' 
rvert  iit  till'  njiiMT 

tical   liiii!   of  any 
ree    equal    i»ai'ts. 
(Irawiihori/.initiil 
ical  lint'.     Divide 
.  into  lialvt's.  and, 
a  vi'i-y  sliiirt  lim-i- 
ic  horiznntal  lines, 
ruling  till' straiglit 
Kintal  lines  at  tlie 
it  losiJ  tlian  atliinl 
veH,  the  remaiuiag 
'  bottom. 

I  Form. 

al  line,  and  divide 
x\  iiavts.  Thron.u'li 
n,  draw  the  lonjiest 
•qual  to  two-tliirds 
line.  Upon  this 
st  the  figure.  The 
ivcle ;  the  acorn  a 
e  whole  is  an  oval. 


I 


COMPOUND  UUIIVKS 


81 


CARD-ExKUCiaK  XXIV. 

Lemon  and  Barrel.  -  The  FUip»e  lUustrated. 

TiKMOv.  —  Firnt    draw  an    ellipsi',   with    its    short 
diameter   about    (wo-tbinlH   ot 
the  length  of  the  bug  diam- 
eter.    .\dd  the  jioints  t'nrmin;; 
the  ends  nf  the  iemou. 

'  Haukei-. — 'litis   is  a   gooi 

figure  for  rlass-analysis  i)efbrc 
drawing.  Thus,  lor  exam- 
ple :  — 

Trnrfii'i:  —  Wli.'it  lines  arc  seen  iu  this  iiguie  ? 

J'lt/iif.  —  J^tiaight  lines  and  curves. 

Tiiir/it')'.  —  What  is  the  position  of  the  straight 
lines? 

I'lijiU.  — Vertieal. 

Tc'ukrr.  —  If  vertieal,  what  else  must  they  be,  as 
they  are  side  by  side  ? 

Piij>l/.  —  \\m]M. 

Tnu'her.  —  What  do  they  represent  in  this  drawing? 

I'lqiil.  —  Hoops  on  a  barrel. 

Teacher. — liut  hoDjts  are  eireular:  tlieae  lines  are 
straight.     How  is  that  ? 

/'uj)i/.  —  When  a  hoop  is  turned  so  we  cannot  see 
through  it,  then  it  iooks  like  a  straight  line. 

Tcdclicr.  —  Is  that  the  position  of  the  hoops  on  this 
barrel  ? 

Pupil.— Yc». 

Ti'dchcr.  —  If  youiiold  a  hoop  with  its  centre  oppo- 
.site  the  eye,  with  each  point  of  the  hoop  at  the  same 
distance  from  the  eye,  what  will  its  shape  appear  to  be? 

Piijiil.  —  A  circle;  and  that  is  its  real  shape 

Tiar/tvr.  — What  is  a  circle? 


82 


tkaviikhh'  manual. 


/.„/;//.__  A  simi.U-  .•nrvo.  It  is  struck  i'roin  oiio 
.MMitri,',  uikI  ImmmIs  ;ililic  ill  all  l>iii<s.  ■ 

y,,,„,/„,,..  _\Vli..n  a  liLop  is  vif\vi'<l  (.l)li<iucl.v.  wliiit 
(l.ics  its  sliapi'  apjM  ur  to  In- '.' 

I'll/)!/.  —  All  I'ililisc. 

Tri'c/in:  —  Wliat  is  an  fllilisc  / 

j^„j,;/  _  A  .(.iiiiioiiiul  cnrvi'  stmcU  from  two  toci. 

7V;,rA(T.— Aiv  till-  fiuvcs  ill  this  drawing  siiiipK 

or  coiiiiiounir.'  ...11, 

y^^^V.  —  Coiiipoimd;  iM'causc  tlif  suU's  ot  tin-  h.xv- 

rcl  are  parts  of  an  fliipsi'. 

2v,/.7//;'.—  llow  lines  tlu(  transverse,  or  Ion},'  diani- 

etiT  (livi'le  tlit-  ellipse? 

/>„„//.._  Into  two  .M]nal  similar  parts.  ^ 

T,;,r/irr.  —  Wliy  do  you  say  i''/iiid  and  ,sv/»(/"r  . 

/V,,,7  _  15,.causi;  "  eipial"  n-fcrs  to  area  on.y; 
'•  similar"  to  shape  only.  Two  iifjures  may  he  equal 
in  area,  hut  of  ditt'erent  shap.'s;  or  they  may  he  simi- 
lar in  sliape,  hut  of  ditVerent  area-. 

2\,,(rf,n:  —  \low  does  the  conjugate,  or  short  tliam- 
eter  divitle  the  ellipse? 

/>„,,//.  _  Into  two  equal  simihir  parts. 

2' „,,•/( ,;c.  —  How    do    hoth    diameters    divide    tlie 

ellipse '.' 

l>„niL  —  Into'  four  eiiual  similar  parts.  ^ 

7V„rA,r.— ITow  (h)  the  diameters  divide  eaeh  other  i 
riinil.  —  Into  halves. 
Ti-Airher.  —  How  do  you  tiiid  the  two  toei,  or  eeiitres, 

of  the  ellip.se?  ,.       ,.  i 

/j„.,//._|5y  drawing  an  ohli(jue  line  from  an  end 
of  the  short  diameter,  on  either  side,  to  the  long  diam- 
eter, the  ohlique  lin.^  heing  eijual  to  one-halt  ot  the 
lon.r  diameter.  Tln^  points  where  the  ohlique  hues 
toudi  the  long  diameter  are  the  foci  of  the  ellipse. 
2V,„.//t'/-.— On  what  does  the  shape  of  the  ellipse 

debend  ?  ,     ,         ,     .-  ..^    t 

P„IjII  —  On  the  difference  m  the  length  ot  its  diam- 
eters. 


lick   i'rom  iiiio 
>li(iucly,  wliat 

roiii  two  foci- 
awing  siiiipW". 

Ifs  of  tlu;  bar- 
er long  (liivni- 


to   iiri'ii   only ; 
iiiiiy  Ih»  ciiual 
)'  iniiy  1)1'  J-imi-     j 

or  sliort  (liivni-     | 

i 

ts.  j 

■rs    (livitlf    the     j 

tH. 

idcfUfhotlu'r?     ' 

I 

I 

foi-i,  or  fciitrcs,     j 

('  from  an  fnd 
the  long  (liani- 
one-lialf  of  tho 
le  oblique  lines 
■  the  ellipse. 
!  of  the  ellipse 

igth  of  its  (liani- 


( o.yfrou.VD  vun  vks. 


83 


Tfiiflin:  —  The  less  the  (liH'ereiiec '.'  — 

I'lijiil.  —  The  more  nearly  the  ellipse  comcf.  to  iieing 
il  I'll'  le. 

Tiuflii'i:  —  The  greater  the  ilitlcrencc '.'  — 

I'djiil.  —  The  more  nearly  it  comes  to  ln'inj,'  a 
straight  line. 

Ti'dvlit'r.  —  How  nnuiy  shapes  nniy  an  ellipse  luive".' 

I'lijiil.  —  .\n  emlless  numher. 

Tiiicln'i:  —  lint  what  may  In-  said  of  nny  point  in 
the  lioiindary-line  of  any  ellipse'.' 

I'lipil. — ■That,  if  a  line  he  drawn  from  this  jioint 
to  eaeii  of  the  foci,  or  centres,  the  two  lines  united 
will  he  cijual  to  tin  long  diameter. 

Trin'hi'i: —  In  drawing  an  ellipse  freehand,  what  is 
to  he  observed  ? 

I'lijii/. — Xot  to  nnike  any  i)art  straight,  imr  any 
part  a  circle,  nor  a  sharp  turn  anywhere. 

Ti'drlicr.  —  Ls  iteverprop(;rN)<;all  an  ellipse  an  oval? 

Puiill.  — No;  for  an  oval  is  always  egg-sliaped  :  one 
end  is  always  larger  than  the  other,  wliich  is  not  true 
of  an  I'llipse.  The  short  diameter  of  the  cival  never 
divides  it  into  two  equal  similar  parts;  but  the  short 
diiuneter  always  divides  the  ellipse  in  that  way. 

It  is  not  expected  th..t  the  teaelnr  will  follow  ex- 
actly thi.;  mode  of  ainilysis.  The  manner  ot'  putting 
the  questions,  and  their  number,  must  be  adapted  to 
tl'.e  <'apiicity  of  the  nupils. 

.Vfter  th(!  prelimimiry  analysi.s.  bringing  out  nmny 
or  few  of  the  characteristics  of  the  ellipse,  proceed  to 
draw  the  barrel  thus  :  — 

Draw  an  ellipse,  with  its  short  diameter  about  two- 
thirds  of  the  long  diameter.  On  either  side  of  the 
centre  of  tlu  long  diameter,  mark  ofi' a  distance  e(pnvl 
to  one-half  of  the  short  diameter;  ilivi'ie  wluit  re- 
mains into  iialves,  and.  through  the  points  of  division, 


I 


H4 


TKAciiya^^'  .u.i.v'.i/.. 


.U,,,v  tl...  lu.a.Is  of  tlu.  l-anvl.     Draw  tlu-  ..n.l-l.no,.H. 
,„,Ui.„  th.-ir  wi.1.1.  ...,.-l    t.,  ..n.-I.alf  of  ....  .,.a.. 

.,,,„:.,   ,,v   .I."    l:-t    divisions.       D.v.lo  t  ...   s,u..o 
,„.,,,„„„   tl...  .....l-l.-r   i..to  four  ...V.'il  l-'^'-t'* ;  ••'' ^^ 

„,„  ,,„„«  i..   tlu.  .■•■Mtr..,  a.ul  tlu,  other  Lo-'PH  .-,  tl,. 
otliur  points  of  division. 

Boitle.  — Ovoid  Form. 

I  )ni\v  II  vertical  lii..',ivi..l.livi.l.' it  \ 
i„to  tluve  ...lual  parts.  At  ti...  I'ot-  i 
ton.,  iiii.l  throuKh  th..  i.pp.'r  po.i.t 
of  .Uvisioii,  ilrasv  liori/.oiitiil  lii."'-, 
luvvii.^;  a  lei.Ktl.  .■«l'"il  •"  «">.'-<l'"''' 
of  the  vertieul  line.  Draw  the  pro- 
til,,  of  the  l.oily,  which  is  Jii.  ..viil 
slif,M.tl.y  lu.MliUed,  aii.l  add  the  neeU 
and  cork. 

CVKD-Kxi^liCISK    XXV. 

EUipw  and  Oval  lUuBtrated.  -  Pear.  Orape.,  and  Ekk- 

Tho  peav  (<»)»  whieh  is  ovid. 
the  grapes  (A),  whieh  are  ellip- 
tical, and  the  egg  («■).  which 
is  oval,  are  to  he  drawn  i>y 
judgment  of  eye.  Tl...  teu.:l.- 
Vr  will  draw  then,  thus  on  the 
hliickhoard,  and  will  then  re- 
quire the  pupils  to  dniw  tl.eui 
on    their  8lat..s  without  deli- 

„___^_^^-^        iiito  ;irop(U'tious  heiug  giv<.|i. 

Draw  the  full  outline  of  each  grap.'  at  tirst,  an.l  th.... 


erase  the  parts  which  should  not  show. 


10  «>ii<l-ln><'l>'*. 

of    till"    riJlilfO 
ll>    till-    SIilU'H 

jiartH ;  dniw 

llliops    (til     tilt' 


,  iviul  tlivitlf  it 
.  At  tlic  I'ot- 
•  ui>iii'r  pi'iiit. 
,ri/,itiitiil  liiii'f, 
111  to  uiu'-tliinl 
Dviiw  the  I'l"- 
licli  is  !iii  iiviil 
I  mid  the  iii'di 


ipeB)  and  'Em- 
I,  wliuli  is  oviil 
whii'li  iUH'  I'liip- 
i'«t,'  ('■).  whifli 
)  1)1'  diiiwii    l>y 
yi..    Tlio  toiidi- 
liciii  thus  on  tliu 
id  will  tluni  ri'- 
ils  to  dmw  them 
i.s  witliout  dfli- 
,iis  lu'itif:  ^,'ivt'ii. 
it  tiiHt,  iind  thfu 


I 


i.'OSt POUND   VVKVKH. 


«■> 


.M, Mi.  — Tilt"  vcrticid  iiml  Imri/oiital  dotted  lines 
artM'(|ual  in  ifn^^l')  ^^'''''''  '•"'  I""""'' 
is  hfiiily  onc-tliinl  of  the  widtli  of 
till'  lii.rizoiital  line.  It  will  Ix*  :>o- 
scvvimI  that  tlic  curves  foriiiinjf  tlie 
handle  hiive  ii  semi-elliptical  char- 
acter. This  is  a  favorite  curve  with 
Xatiire  and  with  de.^i<;iiers. 

Oahi)-1Cxeiccisk    XXVI. 

Bosette  of  Ovoid  Forms. 
Draw  a  square,  its  diainete-s  and  diagonal  ;   ar.d 
then  an  inscrihed  circle.     Di- 
vide  each    diameter    into   six 
eqiial  parts,  and,  on  the  central 
divisions,  draw  the  inner  circle, 
which  will  thus  have  a  diam- 
eter eiiual  t(j  one-third  of  the 
diaiiH'ter  of  the    larj^'e  nwXv. 
On  i'ach  part  of  the  iliameters 
and  diagonals,  between  the  two 
circles,  draw  an  oval,  making 
eight  in  all,  and  touching  one  another. 


(iiiKsrioNS.  —  What  is  w  f()m))oiin(l  oiii'vu?  Ad  dlipsc  f 
What  is  tlic  sliapc  of  a  circle  when  viewed  oli!i(|ueiy  >.  Wliat  aiv 
the  diameters  of  an  ellipse  ealled  '  ll«w  .lees  eiieh  divide  llie  el- 
lipse '  What  is  meant  hy  the  foci  of  an  elliiise  '>  How  can  tliey 
be  toiind  >.  How  can  you  draw  an  elliitse  of  «ivon  proiiortions  < 
What  is  an  oval  '  How  do  its  diameters  divide  it  f  Of  what 
may  its  houndary  line  he  .omposed  ?  What  is  meant  by  "  enial  " 
nntl  "similar"  when  applied  to  ti^'uies  '. 


•■  I 


OHAI'TKU    V. 

roMl'OUNl)  (TRVEa, 

itHVRUsMo    <'ri:vES.  —  tiik   ixiek.  —  AnsTitArr 

•  IJHVKS. 

Tiik  ri>ni|Miun<l  iiirvi's  to  wliidi  \vi'  liuvr  altciKlfd 
arc  ciirvcM  tliut  cliangt'  tlicinlircction  irffguliirly  ;  but, 
wluMi  .•iimplcted,  tlmy  ciu'lose  spacf,  iiiw!  tlif  ijiiim-.s 
yivi'U  tlii'iii  itrc  snmctiim-.i  used  to  iiidicatc  tlic  li^uri's 
tliiis  fui'ini'il,  iiuil  .si)iii(!tiiiu's  to  imlicutc  tlie  liouiitlitr.v- 
liiit'u  of  tlio  figures.  In  this  way  tlio  wonl  iHi|»sc 
iii;iy  lie  ap'dit'tl  to  the  .-tpucc  fuclosctl,  or  it  iiiuy  i.c 
liiiiitiMl  to  Hie  liouudarv-liiic  onclosiup;  tlu'  s|t!iiT, 

\Vi>  will  now  iittcnd  to  those  curves  wliicli  Ufit 
only  cliiiiige  their  direcliou  irregularly,  Itut  reverse  it, 
turuiiig  from  the  right  to  the  left,  from  the  left  to 
the  right,  and  never  enclosing  space,  The  two  parts 
of  this  form  of  the  ccujpouiid  curve  may  each  he  a 
simple  curve  struck  from  one  <entre,  or  a  compound 
curve  strud?  from  two  nr  more  ceutre^. 

Draw  two  eipial  circles. 
as  at  .V.  tniiching  each 
other.  Through  the  poiii! 
isf  contact,  draw  a  strp.ight 
line,  dividing  each  circle 
into  two  unequal  parts. 
Krase  the  two  hvrger  parts. 
A  and    tliere  will   remain   a         ^ 

compouiul  reversed  curve  as  at  B,  each  half  of  which 


80 


-  AUSTHArr 

liivi-  iiltcudcil 
•guliirly  ;  biif, 
iw!  till'  iiiiincd 
lie  tile  lij^iiri's 
tlie  I'otiiitlitry- 
B  wonl  i'lli|)Sf 
or  it  \u:iy  Kn 

cs  wliicli  iirtt 
hut  reverse  it, 
)m  tlic  left  to 
The  twu  j)urtH 
iiiiy  each  be  a 


'f 


VOMPOVND  CUIiVKs. 


87 


\n  n  simple  curve,  Iwin}.'  tde  uir  of  a  eirele.  It  will  lie 
Heen  tliiU  tills  «on»|H>uii<l  i  un'e  lnm  tlio  Hunie  decree 
of  curvature  in  ull  it*,  jiai.  i,  l)Ut  tluit  the  ilireetidii 
dl'  the  eurvo  is  in.Htiilitly  reversed  at  the  |iniiit 
vvlierc  t\:v  ?<tntigl»t  line  tliviiles*  it. 

Iimteiul  of  partr*  of  eirele^.  the  reversed  curve  may 
Iw  inm|Mt«ed  (if  i»urts  of  ellipse-,  or  (larts  of  ovals. 
Kach  of  th«'  two  .•<«>(  tions  of  rhe  curve  w<Mild  then  l>e 
coiiiinHisid  in  itself,  A^ruiii.  cacii  M';j!nieiit  of  the 
reversed  ciirvf  iii.iy  iie  '.juiie  ditVci'.'iit  from  any  one  of 
the  eoninound  uurvee)  winch  lia\c  yet  heeu  de^c^il(ed. 
It  may  '-"'  «f  '""■^'  **  eharactir  that  it  <im  he  struck 
l>y  iiie<!ha!iieiil  means*,  or  it  may  he  what  is  sometimes 
termed  a  '•  I;anrl-curvc.''  hoeausi'  it  has  no  uiathe- 
matically-deiiiied  fealuics,  and  is  struck  l>y  hand 
without  tlse  aid  of  iuHtrunieiit-.  Tu  thj«i  last  varii'ty 
heloii;4  the  tirst  thrse  curve.s  shown  at  T 

'i'he  first  curve  at  ('  i.s  eaUed 
the  <^gee,  and  .-otnetiuus  tlio  "  line 
nf  beauty."  li»  two  icgments  are 
alike.  The  tle^jree  of  curvature  o1 
each  U  greatest  at  the  noint  of  its 
f,'reatest   iilutJide,  and   grown   le.s.H  u 

and  losf-  from  tlu*.'  jiojut-  Ah  v/f  niijuoach  the  ]Hinit 
where  the  eurve  changes  its  direction,  it  beeonicN 
nearly  u  straijjht  line.  Each  s.-jruicnt.  therefore. 
is  a  iinely-graduated  oomjiound  cinve :  and,  the 
two  segments  unite  wit'iout  any  siuMen  chan<.;e 
of  direction  in  the  eurve.  Let  this  be  earefidly 
noted  and  remembered.  Where  the  segments  ot 
the  compound  curve  at  P.  unite,  th.-  direction  of 
the  eurve  is  instantly  and  completely  reversed.     This 


9mm 


mwm 


88 


TKAVtl  Kits'  HAS  UAL 


iniikiM  11  Honu'wlidi  <1iHa>jrpOftlih'  impii'K.tioii  iipnti  tlio 
(•>•<•;  l.iil,  wIhti-  the  HfjjiiH'iits  ol"  tlif  lirnt  (MmiM.iiiMl 
.iirvf  lit  (;  miiti',  tlicri-  i*  no  hui'Ii  iil)ruiit  cliuiiKf  <>f 
ilircftioii,  iiiul  llu"  iiniiivsHidii  niiidc  upon  tlic  «•>■••  in 
.•..iiscqiMiitly  a^ivi'iil'l.-.  Thin  is  HoiiictliiiiK  to  l>o 
..l.s.Tvnl  ill  ilriiwiiin  voiiipoiiinl  curvcH  tiTi'luvii<l,  if  we 
wuiilil  iiiivk*'  tliciii  licaiitit'iil. 

Let  till'  "Ki'f  lit'  ri'pc;iti'(liy  ilriiwn,  until  piijiiis  :ir<' 
f'liniiliiir  witii  its  t'eutiirt's.  Kirst,  dniw  :i  stniinl't 
line  for  the  biwf,  iiiitl  lialvf  it.  Hf(,'iiiiiiii(,'  iit  oiu'cml 
of  tilt'  liiw,  thaw  tin-  lurvc  tlirouK'li  tin-  ci'iitrc  ot"  tlu' 
Icisf,  iiiid  tli)  iii>«  stop  until  till'  oilier  i-nd  is  rrarluil. 
Set'  tliiil  tln-rc  is  no  miililun  cliaiiH"  ol'  .lin'ction  in  tin* 

furvc. 

Till-  si'cond  iinil  tliird  ciirvi'H  sliown  at  V  arc  inodi- 
lloations  ol'  tin-  ogee.  In  tlit!  hi-coiuI,  tln'  iippiT  cud  of 
tin-  iippi'V  Hi'Kiiii'nt.  and  tho  lower  end  of  the  lower 
HeRmeiit.  are  drawn  fuller  tlian  the  other  puts  ;  wliilo 
just  the  reverse  is  triiv  in  the  third.  I5ut  ohserve, 
that  as  ill  the  oKi-e,  so  in  these  eurves,  there  is  no 
«udden  «;hair;,'«  of  directioi..  In  drawing  these  curvei*, 
proeeed  as  with  the  ogee. 

To  draw  the  fourth  form  in  (\  whieh  is  a  uni  n  of 
straight  and  curved  lines,  first,  draw  a  vertical'Iine. 
Divide  this  line  into  four  equal  parts.  and.throuK'i  the 
central  [loiiit  of  division,  draw  a  horizontal  line  eipial 

to  one-fourth    of  the  vertical  line.     Draw  tl urves 

and  straight  lines  as  shown.  Ol'servo  that  the 
straight  line*  so  run  into  the  ciirve>.  that  it  is  iuijios- 
sii.le  to  tell  where  the  former  terminate,  and  the  lat- 
ter liegin.  This  is  as  it  .should  be,  if  wc  would  have 
our  lilies  l.eatitiful.     Were   tho   points   of  junction 


<«ion  iipnii  tlio 
IrHt  i'iiiii|iiiiiti<l 
ru|it  cbuiiiti'  of 
Mtii  tlic  <',V''  ii* 
'tiling  t"  l>i' 
ivc'liiiinl,  if  Wf 

iiHl  iMijiils  !ir<' 
i\v  !i  stnii^'lit 
liiiK  iit  oiit't'iid 

'  CCIltl'l'  of  tlic 

I'lid  Ih  rt'nclicd. 
lirt'ctioii  in  tho 

lit  ('  arc  inoili- 
ic  upiiiT  end  of 
1(1  of  till!  lower 
■r  pirts;  wliilo 

15ut  ((llHlTVf, 

't'8,  there  is  no 
in  these  ciirvt'», 

h  is  a  nni  11  of 
11  vcrticiil'lino. 
ml.  throu^'h  tin- 
mtiil  line  t'(iuiii 
raw  till'  curvi'M 
I'rvo  that  thf 
hat  it  is  iiiij^js- 
i',  and  thi'  hit- 
wo  would  have 
ts    of   juiit'tioii 


VOMPOISU  VUHVKS.  W 

eiinily  diMtiiiKiiiHlml.K',  the  •■IV-.l  w.Mild    Im-  imiHi  h-:  h 
|il,;i>iii«.      lift  tlii'^  |.riiMi|»leof  lii-ftiity  he  reiiinnlMnd. 

In  I)  wi'  hiivf  lit  her  vii- 
ricticH  of  the  rcvcrsiMl  IhuhI- 
riirve.  'I'lie  hiisc  is  divided 
into  third-*  inxtead  of  lialven. 
To  draw  fhesi'  lurvi-s.  pioct'cd 
114  with  tlu'  np'i'.  hraw  the 
whole   liiH'  witliDiit   (*ti.|>iiinf,', 

and  iiiiil< '  altrupt  eliaiij^e 

in  its  direetiiiii. 

It   will  tliiiM   ho  seen   how  u. 

eiiHV  it  is  to  prodiiee  a  nreat  variety  of  reversetl  curves 
hy  ehaiiKiiiK  ^'"'  divisions  of  the  hiwe  line,  or  hy 
niodifyin-,'  the  eiirviiture  of  the  separate  se<,'iiieiits, 
I'lipils  should  fiei|iieiitly  draw  these  curves  and 
inoditieatioiiH  of  theiii.  The  eontoiir  of  articles  of 
glassware,  crockery,  &»;.,  is  usually  composed  of 
curves  like  these. 

Reversed  Curves  applied  to  Vaaea,  fto. 
A  Vask.  —  Draw  a  vertical 
line  of  any  i;iven  leii;;th,  ami 
divide  it  into  three  ecpiiil 
parts.  Through  llie  extremi- 
ties of  this  line,  draw  two 
horizontal  lines  eijual  to  one 
third  of  the  vertical  line,  ami 
extendinn  equally  on  either 
side  of  the  vi-rtical  line. 
These  hcri/.ontal  lines  will 
give    the  width   of  the   top  ami  hottom  ot  the  vase. 


IMJ 


IK-iCUNHH'   HANI  A  I.. 


Join  till'  tinU  "I  Oic  liuriisontiil  liiu's,  nivinn  in  i.l.F'>h)t 
»*«  till'  nt'oiiiotririil  liiiHi  liir  llu>  ili»i^'ii,  IHvidc  iIm> 
liist  vtM'tiful  liiK"  into  tlMi'iln,  lunl,  tlirnunh  tin  niiiitr 
(ll*'i»lonH,  timw  the  iiirv.-  />  in  I).  'I'lu'  IwikIiIi,  ••t' 
CO  iiwc.  niij;Iit  liiivt'  lii'i'ii  Iftkt'ii  1»?!«m  or  ymftnT, 


I'mw  tin'  vt'rtiiul  liiii"'.  itml 
iliviilt-  tlii'ni  iiH  in  tin'  lii'l  I'X- 
1'H'iHt'.  I'hf  t•nl■^■l'  '■  in  I'  lor 
•  111-  contour  of  tilt'  viiHc.  A'ld 
tlio  liori/oiititl  iihi-  lot'  till! 
tottoni. 

Ri>i|iiii'<'    till'    piipils,    ux'm^ 
the  HUinr  I'liivc.  !•>  iliiiw  kiIht 

\  ii^cs  of  ililVrli'Ilt   \\i(|lll>. 


A  Fitobar. 

Dniu  iIk'  viTtiriil  lini'.t, 
aiul  iliviili'  tlii'in  iim  in  tlir 
lant  two  cxcrrisos,  For  tln' 
contour  of  tlio  jiitclior.  nsi' 
ciirvi'  '/  in  I*.  AiM  tlic 
liiinillc  anil  tlic  liottom.  Any 
otliiT  j)i'"'>i>rlii'ns  tliiiii  tliinls 
may  I"'  t.ikrii,  jirovidi'il  tin' 
ri'siiltiiif,'  (li'sitrn  is*  urai-cfnl. 
whic'li  will  ili'iMiid  lai'K'i'ly  "ii 

till'  ihiiwiii^;  of  tlii^  rnrvM. 

It   will    tliiis   111'  si'i'ii    liow  .xinijilr   is  tlic  iiumIi'  of 

ili'«i},'niiiK  '!"'  lontours  of  vasi>s,  artii'li'H  of  tiilili'-wari', 


«■ 


n'lvinn  .III  iil'F'ihj* 
i^'ii,  I)iviil('  lilt' 
roii^h  till  ii|i|i)>r 
Till'  liri'iKltli,  "f 
r  gri'ikt^T. 


•ortital  lini'*.  iiitti 

IH  ill    till'  !:!■<(  I'S- 
rlll'M'   (■    ill   I'  t'nr 

r  III.'  viiMc.     A'ltl 
III    liiii-    r.>i-    tin- 

ii>    pupils,    iiHiii)* 
\i\  til  ilniw  III liiT 

lent    \\i(|lll>. 


■  vertical  lini'M, 
tlii'in  iiM  in  till' 
•rciscs.  I''i>r  tilt' 
tliii  pitclicr.  iiHt« 
1  I).  A.M  tliH 
lie  liottoiii.  Any 
tiiiiis  tliiiii  lliinlM 
en,  proviili'il  till' 
l■si^ll  is  j;riU'ot'iiI. 
Ii'ImikI  liii'ticly  "II 

I'  is  till'  iiiimIi'  lit' 
•li's  (if  tiil>l<'-\vuri>, 


VhMt>offSh  I  I  HthS, 


\t\ 


Siv.  KiU'iiiiriiut'  till'  piipiU  tti  t'M'iii'**'  iIh'ii'  iiivi'iUiuu 
ill  ill-vising  iii'w  I'.iriiis. 

'rhtirv   Im   yi-t    rniMu  •noii^li  Im'  tin'  inipi'iiNinii'iil    of 

fOinilKill     «T«irki'l',V.        Tilis     impliivrlinill      KHI-I      lii'^ill 

Willi  till'  cii'^iilioii  III"  till'  piiiilii'  tiisti'.  muliiiijj;  lulv 
tllill^;s  iinsiilulilf.  With  tlii<  ili'iiiuml  f^r  licUi'r  witrk 
will  ••••iH>'  IIm-  lii'ttir  work.  r>iiiully  it  »'t»*fK  iih  lumi' 
t»  iii.ilii'  an  "liji'i  f  lii'tuitit'n!  tliaii  tmiiald*  it  Innui'ly. 
Iwdviili'd  ulwayx  tliut  tin-  wiirKiiiiin  liii'*  liisti'.  wliitli 
)m  I'llucaMoii   hIioiiM  ^iv'-  liim.      1 1'  ili"'  wiirUinun  is 

iMjt  al»l»>  to  (liftf iiiKuisIi  hctw n  what  i*  liiaiitil'iil  ami 

Wlnil  i«  not.  it  i?<  iiiipoKHilili'  I'll-  liiiii,  I'Mi'pl  I'.V  imri' 
BtH'iiltiit,  to  iiitiUc  any  tliiiit;?  lii'imtirul.  It  would  Im'u 
Miinl  man  sl•('ill^^  llcin'i-  tin'  ni'i'i'Hxity  of  I'lluraiiiiK 
till-  pi'oplc,  us  II  wlioli',  to  a  Just  appri'ciiitioii  "I'  pure 
form,  wliiili  lii's  at  tin'  roiimlafinii  of  nil  licanly. 
WIii'ii  ill.'  lonn  itHt'lf  in  uiinrari'fiil,  liiii'  lliii»<Ii  iiinl  I'li- 
rii'liiiii'iil  must  alway«  fail  t')  niaki- an  olij.'il  lii'iuitifiil. 

A  brtraot  Ourvc«.  -Junotlon  of  CJur»ed  yni  8trol»(ht  Linas. 

Wlioii  riirvi'H  r  pri'scnt 
liotliiiijf,  as  in  tlii-»  v.u'V- 
('list',  they  lit'  ( iillcd  al»- 
Htrtiot.  Till'  iIiawiiiK  of  them 
in  pxi'i'lli'nt  pi  act  ice.  Tlii'' 
lesson  (K)  illustiate-  another 
inipiu'tant  priiunple  in  the 
treatment  of  lines,  if  ve 
woiiM  have  thein  heaiitifni 
AVe  have  here  thi-  siile  juiir- 
tiitn  of  a  eiir>i"l  line  with 
a  strai^'ht   line.      It   will    he 


rea   that   eaeli  curvi"! 


m 


TKAi'llKNti'   MAfllM.. 


lltic,   KM    il    ii|»|inmi')iMi«    till'    virtinil    lliif.   tlmnKf* 
it.   ilirit'tiiMi    li-t    uml    II'**}     mill,    wlifii    if    iiniti-.* 
with    till'    vt'rtiml    liin-.    it    tukf*    tin-   kuiih'   tlin-i- 
(    tlim,  mill  fo  woiilil   ii«>t  <  Mt   iM-nw*   i».  Ii-'wi-vt-r  tut 

itiimci],       Tlii«   i^   .iilli"!    tli-    tuiiK»'iitiul    iiui'Hi 

of  M  nirvt'il  liiii'  with  »  "tminlit  lim'.  'I'hf 
riiXM  \»  niiiih  iniiri'  pl«u»iiiU  ihiiii  ii  wftmt  iitiitiii,  um 
;if  I'",  whi-rt'  thfriirvi'<l  liiii-.  il'i'iiiitiiiinil, 
wiMilil  nit  ilirtrtly  inrnxx  thf  ntminlit 
liiM'.  Sillily  tin'  ililVirt'in  t'  in  i-lVi'i't  ln- 
tw««m  IIh'kk  tw.t  foriiiM  of  »«iil«-jiiiu*tiiiii 
of  Htrili^,'ht  iitiil  I'lirvi'i!  liiH'". 

Ill  ilrnwinn   I'',  ilniw  tin-  viTticiil   liiH* 

I  2  of  iiiiy  K>vi'ii  li'ii«»li.  "iii'l  'liviil''  it 

into  tlirri'  ti|iinl  [mitM.     MuUf  tlii-  Inn-i- 

*'.  /.i.iitiii    lim-  I'liniil   t'<  two    piirtx.      Uriiw 

till-  .|iuiilmiitH  «i»riii.,'iii;,'  iVi.iii  '.'.  ami  ,i'>iiiinK  •!••'  '•i"'l'» 

of  till'  hiiri/'ifittil  liiii'.     Hraw  tin'  I'luninMinil  nirviH 

from  I,  mill  tlii'ii  tin-  M'lni-eirclo  frnni  tin-  ti|.|ii  r  imls 

1)1'  till'  iiiiinlrmitM. 

DetaiU  of  Ornkmant. 

Uniw  II  viTtii'ivl  liin'.  iin-l 
diviili'  it  iiitii  two  i'i|iiiil  piirts. 
MiiUi'  the  \i\>\»'t  liori/oiitiil 
iiH',  wliiili  hIiouIiI  1h'  ilmwii 
u'xt,  n|iiiil  to  till'  vcrtiiiil 
iiiH'.  All  of  <1"'  I'urvi'H  mil 
I'ompouiiil,  I'xri'pt  thi'  two 
Hhurtfwt.  Mollify  tin'  linuii' 
l.y  ii'Vi'iHin^  a  part  or  all  of 
lh(!  curvoH. 


1/.. 

iful  tlii's  rfmn^ix* 
I,   wIm'ii   it   niiiii'M 

ilif  Miiiii)'  iliri'i- 
iM    If,  Imwi'VtT  I'lir 

h•ll^••llHltl  imioii 
li^lit     liiii',      'I'Im' 

11  X4>t'(iiit  union,  n* 
I  liiii-,  it'i'Diitiiiinil, 

rt'ii<t'  ill  ''iVt't't  l»'- 

llA    of    Mil|l-Jlll|l't|l)l| 

i\  liin'!*. 

Av  till'  vrrficiil  liiiK 

^tli,  uinl  ilivitli'   it 

M.        Mllki*   til,'   llDI-j- 
tWn     p.irtH,        I  fill w 

111   j'jiiiiii({  lli)<  i'IkIm 

•    I'lMllpllUIIlt    ciirvcH 

•oiii  till'  ii|>|n  r  i'imIh 


at. 

vt-rtii'ivl  line.  iiU'l 
ktti  two  ('i|uiil  |iurtH. 
i  u|i|K>r  liDri/'Hitikl 
I  hIioiiIiI  Im'   ilniwti 

ill      to     till'     ViTtical 

of  till'  riirvi'H  an* 
,    i'Xi:t'j)t     tilt'    two 

MoiliCy  till'  linuro 
11^;  ti  part  or  all  of 


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CIHM/ICMH 

Microfiche 

Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  canadien  de  microreproductions  historiques 


COMPOUSn  VUKVKS. 


08 


Caud-Kxkk'Isk  XXVII. 
Simple  AbstrftOt  Curves  Balanced. 

Dnivv  I  1'.  uMil  .livi.l.-  it  into  thirds.  Tlirovigh 
till'  liiwcr  point  <ifilivi>iion,  ilrivw 
.'{  4,  fquivl  tu  twit-tiiinls  of  1  2. 
Diiiw  tluMiottcil  hoiindiiry-liue, 
mill  tlii'M  tlif  other  horizontal 
liut's.  Driiw  tlic  ciirvfs  wliich 
iiiiitf  with  the  vi'rticiil  lino  at 
its  silk's ;  sec  tliiit  thi-y  hal- 
iiiK!!'  each  other.  Erase  the 
Jotted  lines. 

The  lines  in  this  exercise 
nii>,'lit  he  u.sed  as  the  construction-lines  for  drawing  a 
leaf;  the  st  'in  beiuK  at  2,  the  tip  at  1,  while  the 
veins  would  follow  th.'  halanced  curves.  (See  card- 
exercise  10,  second  series.) 


Balanced  Abstract  Curves. 

For  a,  div'ide  the  base- 
line into  thirds  ;  for  ft,  into 
fourths.  Ueginning  at  the 
top,  draw  through  the  upper 
divisions  first,  and  draw 
from  one  end  of  the  hasu- 
line  to  the  other  without 
stopping.  See  that  tho 
curves  on  one  si(h^  of  the 
hase-line  are  like  those  on 
the  opposite  side.     Erase  the  dotted  lines. 


m 


ri<  A  VII  Kits'   in  AN  If  A  I.. 


('Aiti.-I'xKiirrsr.  XXVTII. 
Abitraot  Ourveii.  -  Junction  of  Curved  and  Straight  Linei. 
l"iivt(lriiw  tlifci'iitnil  liin-  1  2.  iui<l  divide  it  into 
tiiirds.  Tlit'ii  draw  fi  ('»  and 
7  S  tliroupili  tlic  upper  di- 
vision iukI  the  top,  milking 
tlioni  iMiuiil  to  two-tliirds  of 
1  2.  rill'  ciirvos  from  7  iiikI 
S  lire  (inadrants,  that  is,  (piar- 
tcrs  ot  a  t;irrl((.  Tlie  i-nrvo 
5  4  (■)  is  a  si'mi-cinOf :  tlioso 
sprin^;ing  from  2  ar«  ooin- 
pound  furvts. 


Details  of  Ornament. 

TouM  (I.  —  Hrnw  a  "orti- 
i-al  linu.  Tliroiigh  tlic  tirat 
division,  from  tlio  top,  draw 
a  liorizontal  line  twice  the 
length  of  the  iirat  line. 
l)ivi<l('  this  into  four  equal 
parts.  The  width  of  the 
Hower  at  the  top  is  two- 
thirds  of  tht'  vortical  line. 
FouM  //.  —  Draw  a  verti- 
•al  lino,  and  divido  it  into  two  equal  parts.  Through 
tlic  centre  of  the  vertical  line,  draw  a  horizontal 
liuo  twi<-.'  as  Ions.  Join  the  extremities  of  these 
lines,  thus  formin-,'  a  lozon Re-shape,  indicated  by 
tlio  dotted  lines.  The  curves  on  the  horizontal  and 
vertical  lines  are  compound;  the  otiiers  simple. 


HOMPOVND  CUFVKS. 


95 


:raigbt  Lln«i. 
vide  it  into 
ivr  a  (i  iinil 
'  upper  »li- 
op,  milking 
wo-tliirils  of 

1  froni  7  iiiid 
Imt  is,  <)iiiii- 

Tlit'    ciirvo 
oirde :  tlioso 

2  ATi'    01  nn- 


)riiw  a  ''orti- 
\g]\  tlic  first 
iio  top,  draw 
le  twice  the 
iirat  line. 
I)  four  equal 
idtli  of  tlio 
top  is  two- 
rtical  line. 
)ra\v  a  verti- 
ts.  Tliroujjli 
a  liorizonial 
ities  of  tlieso 
indicated  by 
orizontal  and 
simple. 


rAun-K\EU(tMi;  XXIX. 
Compound  Abstract  Curve*  Balanced. 

iMiiw  I  'J,  and  divide  it  into  thirds.  Make  ."i 
(»  and  "  K  eatdi  eijual  to  two- 
thirds  of  1  'J.  Draw  the  lines 
from  o  and  (i  first,  iind  then 
tho.se  endinj,'  near  1 ;  ne.\t, 
tlioso  from  7  and  8;  Justly, 
tiioso  en<linf,'  near  7  and  H. 

A«  a  ruh',  draw  the  long 
lines  Jir-t, —  those  on  the 
left  heforo  those  on  the  right; 
those  at  the  toji  JK-lore  those 
at  the  hottoni. 

CAuu.ExEitri.SK  XXX. 

A  Vaae.-Boversed  Curves  Applied. 

Draw  a  vortical  line,  and 
divide  it  into  thirds.  :sraKe 
1  2  one-third  of  the  vertical 
line,  5  (>  a  little  less.  J)raw 
1  •'»,  -  G.  Tlirough  the  upper 
division  of  the  central  line, 
draw  ,'i  4.  Througli  jioints 
t3  and  4,  draw  the  curves 
forming  the  outli.ie  of  tlio 
vase.  The  line  forming  the 
lip  of  the  vase  is  to  be  added  abov(!  1  2.  Draw 
the  parallel  lines  in  the  jjositions  shown,  the  up|ier 
one  at  the  bottom  through  the  centre  of  the  ' 
lower  thir.l   of    tlu.'  vase,    and    the   shortest   one  on 


ytj  TKACIIKIIH    M.iMAL 

;     a  VU.S  1.".    n-t   at    it.  -ntr...     Nan.ty  ,nay   I  • 

.,,,.•, I  l.y  ,.U-.n«  tlH..n  u..ar  to^otlu-r  .u  o„..  i.-it, 

ilikI  till'  r.vi'iHi-  ill  aiiiithiT. 

t  will  I t».ut  tiui  n,nt..ur  of  tlii.  v...  ,h  u 

Hli.l.t  niiMlilinvtion  of  the  curves  at  l),in  tl..M.a.lv  part 

t.f  thirt  i'liaptt'V. 

('AiH)-KxK.uni«K  XXXT. 
Flow.r.For«.-Flow.r.Va...-0««  Curve  Applied. 

FiiuM    »/.  — Kor  H'l"  rtow- 
or-fonn.    l-nin     >'>'    <l>-awi.»K 
a  viTtii'al   liiii'  of   any  n'lvvu 
length.     Divide    it    into  four 
eiiual    partH.      Throujj:!!    the 
upper  eiul  of  tlu^  vertieal  line, 
draw  a  horizontal  line  of  the 
same  lengtli,  one-half  to  th« 
ri^ht,    one-half    to    tlie    lett. 
igi^^l^HM^Bv    Draw    Htrai^^ht     li.u's,     nnit" 
;,.,  the  en.ls  of  the  horizontal  lines  to  the  lower  en.l 
o  'the  vertical   line.      Halve    thene    last    hues,   ami. 
irough    each   point    of  .livi.ion,  draw  a  eompon..- 
...we'  with    the  ogee    eharaeter,   the  upper  seg^m 
temling  inwanls.  the  lower  segment  outwanls.       )..  W 
the    i.  ner  eompouml   eurves    from  the    endH  of   the 
lllrizontal  li.ai  to  the  lower  .livi.ion  in  the  vert.cal 
li„e.     Alia  the  short  upper  curves. 

FouM  /.  -  l)nt.v  u  vertical  line,  of  any  given  length, 
.,,1  <li;i.le  it  into  four  equal  parts.  Make  the  top  o 
■the  gL  one  part  wide ;  the  greatest  width  of  tl:e  bowl 


iij>j»cr  tliinl. 
irt'tTcnt  piirtrt 

•icty  iiiiiy  '»•' 
r  ill  t»iu'  ii''iti 

tlii««  viifto  II*  u 
tlu!  I'luly  piirt 


irve  Applied. 
I'.ir  thin   rtow- 
liy    drawing 

»)t'   iiiiy  Kiv>-ii 
0    it    into  t'ltiir 

'riiroujjth  tilt* 
10  verticiil  \\w, 
itivl  line  of  tliti 
Kiif-liiiir  to  tln! 
X  to  till'  It't't- 
it     liiit's,     uiiit- 

0  tliu  lowiT  IMItl 
lust  lilH'!*,  iiK'l- 
v\v  u  coiiipotiml 

upptT  segiui'iit 
utwiinls.  l^rivw 
h..    »'iid«   of   the 

1  in  the  vrticiil 

my  piven  length, 
Make  the  top  of 
width  of  tl-.e  bowl 


voMi'ouxit  rrn i-f:s: 


t«7 


Mill*  part  and  ii  hiilf,  luid  one  part  iind  a  lialf  from  tin- 
top.  Malic  *hi' width  of  fill'  Itiitloiii  Millie  a-t  {Kreatext 
svidth  of  the  liDwI. 

l''oUM  »'.  —  Driiwti  vertieiil  line,  of  any  niven  Icnjfth. 
and  divid  '  it  into  thirds.  Throin,di  the  hiwer  end  of 
the  vertieal  line,  draw  a  hori/ontai  Hiic,  making  it  ei|iial 
to  two-thirdft  of  tlu'  vertical  line.  From  the  upper 
division  of  tho  vertical  line,  draw  ohliipui  Mtrainlit 
lines  to  the  ends  of  the  liorizoiitiil  line,  On  these 
ohiiipic  lines,  draw  the  conipniind  curves  fi)riiiiii^{  the 
hell.  Add  the  liandle  on  the  iip|ier  third  of  the 
vertical  line,  and  the  touguu  htdow. 

C.vuiJ-K.yKiiti.sK  XXX II. 

Four-pointed  Stsr  and  SQuaree. 
I)raw  two  straight  lines  of 
any  given  eipial  length,  ono 
hori/ontal,  oiu^  vertical,  uiiil 
hisecting  each  other.  Divide 
ea<'li  half  of  each  line  into 
twoecjual  parts.  Through  the 
points  of  division,  draw  lines 
forming  a  sipiare,  iuiviug  its 
sides  parallel  with  the  jirst 
lines  drawn.  (Joiinect  the 
same  points  of  division  by 
oI)li(pu'  lines,  forming  a  second  sipiaro  within  the 
first.  Divide  tlie  sides  of  the  first  sipiare  into  three 
equal  parts.  On  the  Cc'ntral  part,  draw  isosceles  tri- 
angles, with  their  apexes  ut  the  cads  of  tin;  first  two 
lines  drawn.  Add  the  circle,  which  will  test  the 
accuracy  of  the  drawing. 


98 


TKACIIKIIS'  MAMIAL 


<;auI)-Kxk.im:imk  XXXIII. 

Vui>.— The  ORa«  Ourva  Appllad. 

Diinv  ;i  vcrliiiil  lint'.  QiiiirfiT  it.  I'liroti^li  cncli 
i'IkI,  <lni\v  11  ImrixoiiUil  liiit>  oii«>- 
liiilf  us  lonn  us  the  Vfrticiil 
liiii',  iintl  cxtt'iitliiij;  t<f  tlic 
^.ilm^•  tliMfiiin'i'  (III  citluT  xiilc. 
Dmw  iwo  i)tln'r  vcrticul  liiit's*, 
uiiitiii),'  (III-  i'ikIm  (if  till'  Imri- 
zoiitii!  liin'«i.  l>ivii|i'  till'  liiHt- 
ilriiwu  veitinii  lines  into  two 
i'(|iiul  piirts;  ami,  thiDiiuli  t'licli 
point  dl'  division,  ilniw  a  >'<>in- 
|ioiMitl  tuivc,  liaviiiK'  till'  ot,'i'f  iliariirttT,  to  coiiii«Mt  tliP 
end  of  till'  liorizintal  line  al.ov.'  with  tin-  uiitl 
of  tlu)  liorizontal  lino  li"lovv.  Make  tlie  altitudf  of 
the  curve  at  ;li<'  ceiitie  of  each  se^'lllent  <(|iial  to 
one-half  of  one-r.nirtli  of  the  vase'n  liei^ht.  Add  tho 
hottoni,  nialiin^  the  widtli  of  that  and  the  width  of 
the  hands  e(|nal  to  oiic-foiirth  of  one-fourth  of  the 
vase's  heiglit. 

(;ai{u-Kxkk(;ise  XXXIV. 

A  Hosette  oompoaed  of  a  Olroto  and  BeRinsnts  of  Clrolei. 

Draw  a. square,  its  diameters  ami  diat^onals.  Divide 
the  diameters  into  six  equal  parts,  and,  throuj,'h  the 
inner  points  of  division,  draw  a  eircile.  Draw  ohlicpiu 
lines  to  form  tho  other  diagonals  of  the  four  small 
H(piares.  Divide  tliese  last  lines  into  thrtH!  equal  jiarts. 
Using  the  last  linv's  us  bases,  draw  on  their  inner 


roiigli  )'m'1i 
111  liii<>  oiii'- 
Ii(«  vt-rtiriil 
lljj  to  tile 
I'itluT  niili'. 
rtinil  lines, 
r  tin'  Imri- 
|i>  the  liiHt- 
H  iiitio  two 
ii'du^Ii  caoli 
liiw  II  <'i)in- 
coniu'ft  tilt' 
li  till'  fiiil 
iiltitiiilt'  ut' 
t  t-qiiiil  to 
;.  A(l«l  tlio 
In-  wiiltli  of 
iirtli   of  tilt' 


ta  of  Olrolea. 

ill.-*.    Diviili! 

Ihroiii^li  tlio 

)i-ii,w  oblii|Uti 

four   small 

equal  jiarts. 

tlit'ir  iiiiiiT 


i 


COMPOUXn  I  tttiK.S. 


1(1 1 


niil***. -.impl.' .iirv.s,  to  .oiiMii  t  r i,i|»   .,|   tli,.  •lium 

vU'tn  ot  llio  larj^ti  ii<|Miir)>,  aiiij 
Witii  their  K'eatiMt  uUifiuli'  at 
till'  eeutle,    ami    tourliili^'   ||i  . 

eirfuiiifert'iMi'  of  fho  .jii  I.' 
alriMuly  tlrawD,  I-Vom  tlir 
aiiKlei*  of  tlu<  larKC  *|uure, 
mill  fi'uiit  till'  eiiiU  of  it.H  ill. 
iiiiictent,  draw  Hiiii|)lc  ciirvtH 
to  the  points  of  ilivJMioii  on 
tile  iliayoiiuls  of  the  Miiail 
M|uare(<, 

<JAKi».|:xKii<ir^|.:  XXXV. 

Tba  Amerloan  Flmg. 

F)ravv  the  xtalV  and  oiitlinr 
of  the  tlaj;.  making  the  latter 
Hli^htly  ol.loii^r.        Divide    the 

height  of  the  llaK  into  thirteen 
equal  jiarts ;  from  the  i»oiiits 
of  division,  draw  liori/ontal 
lini'8,  tliiiM  forming  the  barn  or 
«trilie.s.  Let  the  Held  for  the 
stars  take  up  seven  of  the 
stripes  in  depth.  On  this  tidd 
draw  thirteen  stars. 

Theiminherof  ori^fiipil  States  was  thirteen, 
are  always  thirteen  .stripes  on  our  national   tla^       , 
re.senting  the  thirteen  original  States;  I.iit  a  new  star 
is  always  added  for  every  new  State  admitted  into  the 
Union.     The  copy  has  thirteen  stars,  for  the  thirteen 


Then, 
•ep- 


|OII 


1f;.lillKHS'   }t.\SrM„ 


H-  iiuuiy  -tur-  a.  llM-n*  ur-  Htut.-  ut  tlii»  tun... 

(  xiiit-KxKUiiMK.    XXXVI. 
BiRht'poinMd  8Ur. 

Dniw  It  Hi|uiiri'.  nnd  i«iiIm11» 
i,|f  it  iiit.»iiiin-<'i|iiiil  >«|iiur«'i». 

Diviili-  tiicli  xiilf  «•!'  ill"  >*f''<'i- 
mil  H.iuuri' int. ttwociinnl  part ». 

|»raw  an  iilili.|in'  liiu-  lr<>m  llif 
(•.•iitriil  point  of  <livi«ii>ii  «>il 
..ii.li  ».i.lf  to  fii.'li  an«l.'Oii  tlit> 
i.ppoHitf  nidi-  <tf  till'  ».(iiiun«. 
It  will  I"'  "•••'"I  ♦'"'^  ♦'"'  »*'"!'"• 
..!•  M|.ian'*   M.rvf   tu   ti')*!    tl««. 

uituracy  «!  •'"■  work.  # 

('AUi»-KxK«(  l««i:    XXWII. 
A.  Houte, 

|)nv\v  a  vi'ilicul    lii"'-    I    -• 
nf  iiiiy   «ivt'ii   li'ii'^tli.   anil  tli- 
vi(l<'  it   iiilo  lliirtU,     'riiioUK'l" 
tin'   nppi  r    point    of  ilivi^ion. 
draw   a    Inni/ontiil    iin<'.   Ti  ('.. 
of    till-    naini-    Ifn^tli    an    tin- 
viTtical  lini'.      I>iaw  a  Minilar 
liorizontal    line    tlirouuli     tin- 
low.T  'Mnl  of  til.'  v.Ttical  lin.-. 
^^_^___^^^__    Draw  vi-rtii'al  lim-'*  coniu-ctiny 
\     tin.  ..n.l-*  of  tin.   l.ori/ontnl    lin-..       Divi.l.'   lim'  7  H 
'     into  four  ..p"^!  I''>'»-      l'"'"'"  ^''"  '''^^''  '""^  ^"^''  ^'"""'' 


VUMI'nCSh  Vt'Ht^.s. 


m 


i»  rtiiu  with 

nil'. 


mill  miiIhII- 
|iial  »«|iiiirt'K. 
il'  llif  or'i^i- 
ii'i|iinl  piirtH. 
iiii-  Irxiii  tilt" 

lliviKJDll  oil 
UIIKIi-  oil  till' 

tlii>   M]iiurc. 

At  till'  »«iiiikn- 

tu    tl"»l     tl'f 


III    Uw:    I     •_'. 

i^tli.  iiimI  <li- 

u.  'riii'tiiK'i" 

of  ilivisi'iii. 
ul  lilK'.  Tt  «■(. 
ii^tli  iiH  tin- 
iriiw  !i  siiiiil'ir 
tlirtni;,'li  tin- 
.  viTticiil  lilif. 
icH  coiiiu'ctini.; 
vidi'  liiii'  I"  ^ 
iiiil  K'it  jioiiitH 


III'  ilivi«iiiii,  iImw  iipwitnU  IW"  vi-rtii-ul  liin'>t  of  ll»» 

KltllH'     ii'llUlll     it"     I     '•'.     till'     llrf>l     Vl'l'tirill     lllli'     illltMM, 

Draw  II  liiiii/oiitiii  liin  loiuiii  tinx  llir  ii|>|m  r  i-ihN 
III'  tlii'si'  two  viTtii'ul  liiii'H,  iiikI  tniimiin  iIm'  ihIui' 
of  till-  limimt.  Kroiii  tin-  ciiiU  i.f  tin-  Imri/itnlul  Iiih', 
timw  iililii|Uii  liiM'w  for  till'  niiif.      Hw  ilmt   ilif  roof 

|iiiiji'ftH  mimfwlmt.     Ailil  tl Iiiiimfy, '.».  <•.     MuKi- 

llii-  wimloWK  mill  iliior  two-tliii'iU  uw  wiili-  iiwuiii'-fnuitli 
of  till'  wiiltli  of  till'  liiHMi'.  Miikf  tliM  liiiulit  of  till' 
ii|i|iiT  wimlowH  li  littli-  li'Hi  tliiiii  till'  lifiirlit  of  tliii 
k'wi'r  wiiiilowM.     Fiiiinlt. 

t'.\HI|.r,XKU.  tSK    XX  Will. 

A.  JuR.  -The  Rlllpua  AppU»<l. 

Mriiw  II  vrrtiriil  lim-  of  any 
^ivi'ii  li'ii^rli.  TliroiiKli  itx 
ri'iitri',  ilmw  It  liori/.oiitui  liin' 
iwiHtliirils  iiH  loiiKt  hihI  |iri>- 
ji-rtiii^  to  till'  Hiiiiiii    tliHtmii'i- 

■  III    I'lirll     -^idi'    of    llic    VlTticill 

liiii'.  I'HiiiK  tlii'Ki'  two  liiit'H  uH 
till'  ilimiii-ti'i'H  of  mi  rlli|Hf, 
ilmw  till-  I'liip.ti'.  Muilify  tlii' 
i'lli|)si'  to  fiii'iii  tile  liiidy  of  till* 
jit({ ;  mill  tlic  limiill''  mnl  mrk. 

('.\iiii-l''\KK(  isi:   XXXiX. 

A  Vase.  -  VivlaUoni  of  tho  Okbo  Curve. 

Drnw  1  L',  ami  iliviili-  it    into  tliirii^.      Uiiiw  .'I    I, 

(•i|iiul  to  two-tliirds  of  tin-  vcrtiial  liiir       hriiw  ipMii|Ui' 

liiii'i«,  juiiiiiig  the  I'lid.s  of  tlii'  1i(iii/oii;;il  line  «it!i  'In- 


m 


TKVHKHh'  V4.Vr.IA. 


iHttliMU  "I  lltf  vi'riii'iil  liiitt.  TliiMUKh  tUv  |Niiiiia  >t|' 
>liUKi<iii  Kii  till'  vcrtii'iil  III))', 
<!i'iiw  lii>ri/<»iihil  lihi'*.  i)t  tiHii'li 

iIm'     nli|l<|l||t     Ii||»«,        |>ruW    till' 

I'  iiiiiii:iiiu  liorijiiirilitl  liiii'it  | 
iiiiki*  IIm'  l)Uf<i>  iM'urlv  i>i|iiiil 
!'•  itiii'iialt  <>!'  tlitt  llt•i^||t  III 
iIm>viiiii>.  FihUti  l>y  ('iiri'dilly 
IrikMiii^  ill MM|Hniit|  t'lirvi'N 

wllirll  Intlll  llli'   fitlllolll'    III'   till' 

N.tii'.  Mil*  tliiit  till'  I'lirvi'w 
iiiiiki'  II  liiMtiitil'iil  jiiiirtiiiii  Willi  ilii- •truiclit  liiti>»  iit 
•1  It.  '{'Ill'  ii|i|ii'i'  riirvi"*  itii'  li  hliu'lit  viiriatioi)  nl'  iIh' 
■  i({r>>.    till)    |ii\U'r    iii-({llli'lltn    lii'ili^    li    ll'llli-    illlli'r   tllllll 

till*  ii|i|ii'r  uiii'>«. 

t'\iii>-l'!xr.t(ri»K.     XI.. 
Tti«  Orumli  k'ikii- 

hi'uwilii-HtiilViit'tlii-lliiKltrMt. 
Till'  ii|i|M'i-  mill  lower  liiH'fi  III' 
till'  lliii.;  lU'i' I'liiniiofii'il  III  I'liin- 
|iiiuiiil  I'lirvi'A,  liiul  till'  I'llj^i- 
lai'lln'Ht  I'liiiM  till-  xtitl)'  i.'4  u 
M'i'tii'iil  liiH'.  I'll!'  iiiiiiih-jiii'k 
iiciil|ii"H  iiliiiilt  iilir-li'llllll  III' 
till'    Wllolf     llll^    (MI'I'll     ill     tlii>« 

\ii'W).       hniw    till-    liinii    iit 
till'   ii|i|M't'   I'i'jiit-liiiiiil  niriii  r 
ill  wliicli  till'   liiii'K  rui'iiiiii^  till'   jiK'k  lii'i'  iiliu'i'il,      ItH 

•  iiil^lltluU    lilnl    lliuilM'tlMfl,  with    tun    |iUI".ilfl    liiii-M    on 

I'lU'li  ftiili',   will  n'wi-   till-   oiitliiii'   ul"  till'   luH'H.      Tliu 
iliaillrti'l't  mill  ilillitolillN  In  In-  tlirh  I'l'itKi'il. 


|M>l||ta  itl* 
rlhlll  IllM', 
•,   hi    titlh'li 

hriiH  ill)' 
ul  lihi'it  I 
itrly    i>i|ii(ii 

lifiuht  ot' 
y  vnrvUiWy 

IIdI  rlirVfH 
oil  I  III'  ttll> 
III'       rllI'VI'l* 

lilt  lillI'M  Itl 
iilll      III'     till' 

liilli'i'  tliuu 


ii'llitKllrNt. 
■t-r  lint'*  III' 

I'll   III'    I  Olll- 

till-   I'll^i' 

ittull"   i*  Ik 

iiniiiii-jiii'k 

-liMiiih    111' 

I'll   ill   tlii" 

'      tnl'lll     lit 

mil  riiriii'i' 

lii I.     \l» 

I   liiii')«   lilt 

nil's.  'I'llL' 


VUMl'itV.Xh  VI  HVttik 


Oftrlyiiiii  rorma. 
I>rikw  II  vi'rtiriil  litii',  III'  any  i:ivi<ii  li>nK(li.     |)|vii|i> 

It        iittil       nix       )'(|I|||I       |il||-t>>. 

TliMii^li    tilt'    ri'hirul    |i>>ihl 

III'  iliuKiiin,  ilriiM  11  liiin/iiti- 

likl   IhiM  twiHihirilH  UN   liiiiK 

ikM    till-    vcrtii'iil    line,     ami 

iliviilii     it     into     >ilx     i'i|iiul 

purtM.      Oil  lliiKii  iwii    liiii'i. 

iM  iliitiiii-li*ri«,  iiiiiMtriii't  lui  nil- 

liMi((,    iiinl     ilrusv     itt    iliii^- 

iiiiiiIh.     With   till'  I'liiU   mill 

nit|im  of  tliti  olil'jiiKit  itM   liiiMfM,  ilriiw  i.iiii|ili'   riirvf^ 

iIiiiiiikIi  till-  outiT  poiiitM  iii'diviiiiiiii  till  till*  iliuiiiftiTK. 

hraw  HJiiiiiitr  riirvrx.  iiiiiiii'itiiiK'  tin-  ailjiii'tiit  i'IhU  nl 

till'   iliaiiii'ti'i-'*   mill  ti'iiiliijj;    iiiwuril".       Mr.iw    ullii"* 

niinilur  mm'*,  ti'iiiliii>{  iriwunlK,  ami  fniiiii'itiiiK  •!'" 

ailjiu'ciit  iMiiiiti  III'  iiiti'i'M'i'tii r  tlif  la-l  iiii'M'h  with 

tlui  tlia^iiimlii.  Kraxi'  tin-  ilntli'il  liiifi.  ami  tliimi'  (mitu 
t>r  till'  llrnt  mirio*  dl'  iiirvi'H  wliiili  |ii|.<4  umliT  tlm 
wu'oml  HiTit"  Tin-  witltli  ol"  tlm  horilir  I*  ••iii>-linll' 
of  oiiu-Nixtl'  "i'  till'  vcriii'til  (liuiiititfr. 

('Allli-KxKUriHK    \MI. 

DoK-tooth  Moiitcling.      Ii.terUolnK  rorma. 

Draw  tw<»  Miiiiart'^  lyiiij^  i<ii|i<  hy  hIiU-  liorizontully. 
Iiiit  mil  <|iiiti>  tiiiuliiiij,'  rai'Ii  ntln-r.  l)iaw  ltii>  iljiiiii- 
•'ti'i'H  uinl  diaKKiials  ;  ailil  llu-  >lij'lit  iiiili'iitatimiii  at 
tlio  I'liUd  of  I'ui'h  iliaiiii'tiT.      Kium-  I  In'  lliiHlK'tl'^•^  and 


i 


104 


V>.IC7/r;/.'>'    M.\y('A!.. 


ilraw  ;i  i.!U"ill<'l   liii<'   aliovti    and  Ixi.w,  ax    in   oiImt 
iiiniililin^s. 

Draw  a  .-(luiirc  ami  its  «lia)i- 
uiials.  Cut  ntV  a  Irillo  IVoiu  tin- 
(■nils  ()('  cacli  (lia^;  iiial.  ( )ii  <'a<'li 
side  of  wliat  remains  "t"  ''ach 
(liaKiMial,  as  a  l>asc,  draw  a 
siii'plf  <'i>vv<',  liaviii;,'  ail  alti- 
tiidi'  fi[\\:\\  to  oiH'-tliird  of  tlic 
scini-dia^oiial.  Iii>idi'  tln'M* 
curves,  draw  similar  jiiiraliid 
.•iirvcs.  Draw  oacli  band  lull,  and  tluui  erase  the  iM>r- 
lions  wliieli  ilo  not  sliow  lieeausi^  of  tlie  interla<-in|,'. 

Draw  a  see<)n<l  s(|uar«!  ami  its  diagonals.  On  o.icli 
>idc  of  tlie  sijuare,  draw  a  senii-.'irele,  joining  tlio 
eorneis  of  tlie  square,  and  passing  tlivongh  its  centre. 
i'lu'U  draw  an  ii.scrilted  cinde.  Inside  these  curves. 
draw  similar  i.arall.d  curves,  except  that  the  curvcM 
parallel  with  the  senii-cindes  must  he  drawn  on  a  part 
,,f  each  semi-dia!,'.)nal  as  a  base.  l>r.iw  tlu!  hands 
full,  and  then  erase  the  parts  which  do  not  show 
hecans(!  of  the  interhving. 


(iiKSTioNS.  — \Vli:\t  is  a  rcvorscil  vww  >  Its  si'^liK'nts  * 
What  iniiv  lie  tlio  <  liariicter  of  oiioh  se>;nuMU  '  M'li  it  is  nioaiit 
\,y  u  liiuiil-cinve  '.  l)»tiil)o  llic  o'^ve.  How  slioulil  tlio  reversed 
ciuvc  ili.ui-e  its  .liivction  to  !).■  l.fuutil'ul  ?  How  should  it  1»; 
.liiiwn'  How  >li<)ul(l  ii  eiuie  inn  into  a  straic^ht  line  for  the 
iunctic!!  to  ho  heautifiil  ?  How  c  ui  tlic  sliapo  of  the  reversnl 
cnirvc  he  rctulilv  niodifie.l  ?  For  wliat  is  this  rnrve  nuicli  used  ' 
Wluit  are  ahstVaet  euives  ?  \Vhnt  is  the  tangential  union  nl 
strai-ht  and  curvi'd  lines  ?  Wliat  of  it?  What  lines  should  he 
draw^.  iirst,—  the  Ion-,  or  sh.rt?  the  left,  or  right?  How  are 
interlaeiii)'  forms  hest  drawn  ' 


IIS    in    dIImt 

11(1  itfl  (liajt- 
ill<!  t'l'Din  till' 
ill.  On  I'lU'li 
ins  lit"  ••acli 
sc.  ilraw  a 
n;^  lui  iilti- 
tlilrd  i)f  till- 

M>illl'         tllCM' 

ilar  i>arallt'l 
ruse  tlic  )Hir- 
itrrlafiiig. 
s.  On  oiich 
joining  tlio 
;li  its  centre. 
liicsc  iMirvcs. 
,t  till'  curvi's 
ivn  on  ii  part 
V  till!  liand.s 
()    not    slioNV 


Its  srj;Mii'nts  t 
\\'\)  It  is  mount 
jlil  tlio  rcVLTSfil 
w  should  it  1)0 
■;lit  line  for  tin; 
o(  the  reversal 
ve  much  usnl  ' 
entiiil  union  nI 
lines  shoulil  liu 
;;ht?     How  i\n; 


CHAITKIJ    VI. 
l'UA("ri(AL   DKSKiN. 

liKOMI'.TKK'AI,    I'AITKUNS,    1 1.1.1  S  m.VTI.N  (J   S  V  MMKTKV, 
ItlU'KTITlO.N,     IIAI.AM  K.    IM'.riiSK.    ItliKADril. 

SoMK  of  the  pri'vions  oxcroisfs  iUustrati-  fninlann-n- 
tal  principlo.s  of  practiciil  dcsiyn.  Miit  as  tln-rt* 
were,  at  tin;  beginning,  so  nniiiy  otln'r  tilings  tn  teaeli. 
it  was  thovight  he.st  to  deter  all  systenuilic  explanation 
of  design  until  the  pupils  eaine  to  tin-  second  series 
of  cards.  It  will  not  l)e  di.licnlt.  even  tor  ipiite  young 
clii!dr(>n,  to  understand  the  principles  wliidi  will 
now  lie  discussed  and  illustrated.  A  knowledge  of 
these  prineiples  will  give  an  additior.al  charm  to  draw- 
ing :  it  will  enable  the  pupils  to  begin  at  once  and 
intelligently,  to  make  original  designs.  Though 
these  prininples  of  design  will  be  found  so  easy  of 
comprehension,  like  the  fundaun-ntal  principles  of 
arithmetic,  yet  their  applications  can  be  madt!  sullici- 
ently  difficult  to  test  the  ability  of  the  hand,  eye,  and 
taste,  which  have  been  tliorougldy  trained. 

Perhaps  it  nuvy  be  thought,  at  the  lirst  glaiice.  that 
sor.ie  of  the  drawings  on  the  card.>-  in  this  series  are 
too  elaborate  for  young  children  ;  but,  if  they  have 
been  fairly  instructed  in  the  preceding  exercises,  and 
are  now  made  ac(]uainted  with  the  principles  of  de- 
sign which  these  drawings  illustrate,  their  execution 
will  be  found  none  too  ditficult,  if  we  would  secure 


105 


100 


m. it:  UK  US'   M.IMAL. 


gdoil  irsiilts.  Wliiit  may  at  lirst  .strike  tlic  inipilH  as 
intricate  will,  cvi-n  to  tiicin.  apjicar  siinidc  ciimi^li. 
till'  iiiiiini'iil  the  iiriiii'iplcs  coiitrDJliiig  tlii>  df^igii  arc 
nnilfi'.Htonil. 


SYMMinUKAI,     VUKANUKMKNT    AltOI'T    A    OKNTHK. 

First  of  all,  tt'ucli  tlie  pupils  what  is  meant  hy  sym- 
metrical :irrant,'i'meiit  al)i«nt  a  centre.  This  re(inires, 
that  whiitever  is  done  in  one  part  of  a  (lesi>;n  .shall  lie 
done  in  all  correspondins^  parts.  When  a  line,  for 
example,  is  aiMod  in  one  part,  or  removed,  lines  in 
all  other  parts  havin;;  the  same  relation  to  the  centre 
of  the  desij^n  mnst  i)e  added  or  removed.  The  mo- 
ment a  line  is  uilded  without  its  corresponding;  lines, 
the  design  is  spoiled,  hecause  there  is  a  violation  of 
the  principle  of  symmetry.  There  must  he  no  super- 
fluous lines.  On  the  other  hand,  every  timo  a  new 
line,  with  all  its  corresponding  lines,  is  added  to  a 
figure,  a  new  design  is  ]troduce<l.  The  new  design 
nniy  he  more  heaiitiful,  or  it  may  be  less  beautiful, 
than  the  old.  Thus  it  frequently  happens,  that  an 
elaborate  (h'sign  contains  ii.  itself,  marking  the  dif- 
ferent stages  of  its  growth,  quite  a  number  of  less 
elaborate  designs,  which  are  readily  discovered  by  an- 
alysis. The  arrangement  of  the  parts,  many  or  few, 
of  every  design,  is  always  determined  by  fixed  law: 
nothing  is  left  to  mere  chance.  Illustration  will 
make  this  clear.  There  is  no  one  so  young  or  so 
stupid  as  not  to  take  greater  delight  in  his  drawing 
when  he  has  been  once  made  acquainteil  with  the  law 
controlling  the  .structure  of  the  design. 


ii|t]<-   t'lmii^'li, 


A    CKNTHK. 

loant  In-  syni- 
riiis  r('(|iiirfs, 
•8ij;ii  .sliiill  l>t' 
II  n  line,  for 
)ve(l,  lines  in 
to  tlic  centre 
d.     Tlie  mo- 
unding lines, 
I  violation  of 
id'  no  snpep- 
tinic  a  new 
i  added  to  a 
'  new  desifiii 
'ss  beantifnl, 
lens,  that  an 
•king  tlie  dif- 
nn))er  of  less 
jvered  by  an- 
niany  or  few, 
ly  iixed  law : 
istration    will 
young  or  so 
liis  drawing 
witli  tile  law 


I'U.iCTlr.M.  ///■..s/'/.V. 


m 


A  CroBs,  aiuatratniK  Syinmutriool  Arrttnucniotil  about  the 
Centre  of  a  3qunre. 

Draw  tilt'  lignre  at  A  on 
the  lilacklioard.  reiiniring  the 
pupils  to  draw  it  with  you,  on 
their  slates.  Tho  exercise 
may  he  conducted  somewhat 
after  the  following  manner:  — 

Tiiir/ifi:  —  Draw  a  f^quan' 
on  its  diagonals  ;  add  its  di- 
ameters, all  in  liglit  line. 

J'u/iI/k.  —  We  have.  _ 

Thi^  puitil."*  will  indicate  tinit  tiiey  have  completed 
their  work  hy  raising  their  hands,  or  in  any  other 
way  the  teacher  may  direct. 


Ti'iif/ii-r.  —  Mark  tin*  centre 
of  the  npjier  half  of  the  u(>p(T 
left-hand  side,  as  you  see  that  I 
have. 

J'kjiI/s.  —  We  have. 

Thia  will  give  what  is  seen 
at  ({  in  R  Having  explained 
what  is  meant  by  symmetrical 
arrangement  about  a  centre,  pro- 


Tfir/ii-r.  —  IIow  many  other 
nnvrks  can  be  made,  having  just 
the  same  position  with  reference 
to  the  centre  of  the  square  '.' 

Pupils,  —  Seven. 


1((M 


TE.WUKItS'    MANUAL. 


•<•* 


'riioii>,'li  tliii*  miiy  111"  tlii'ir  first  lt'H*«on  in  symmo- 
tiy.  s.iin-  i.r  tlx-  |>(i|>ils.  iifViTrliclcss,  will  «ivf  tho 
ront'cl  iili>\vi'l'. 

T'lir/irr.  —  Miikf  the  seven  luWitionul  inarkn. 
I'it/ii/s.  —  We  liavH. 

Tliis  will  give  what  is  seen  at  h 
ill  B,  lesstbe  lioavy  <il)li(jne  line. 

Ti'iiclirr.  —  Now  <lraw  the  up- 
per (pmrter  of  the  upper  lett- 
haml  wide  of  tlie  scpiare,  in  heavy 
line,  as  you  see  I  have  (hawii  it. 

I'li/iils.  —  We  have. 

■["hiswTll  give  the  result  whi.h  is  seen  at  h  in  H. 

7V,„./m/-.  —  How  many  other  lines,  liavinR  the  saino 
ivlutioi,  to  tlie  eeiitre  of  the  square,  .'an  he  drawn  .'' 
I'liplln.  —  Seven. 

Thiit  eaeh  pupil  may  have  a  fair  opportunity  to  eon- 
.si.ler  the  .piestion,  insist,  if  not  always,  yet  certainly 
lit  times,  that  no  oral  response  he  given  by  any  one 
until  a  signal  from  vourself  The  great  art  of  putting 
.piestions  properly,  is  one  of  the  first  things  a  teacher 
sh.iul.l  learn.      I'-ut  to  proceed:  — 

7V,„.A,./'.  —  Draw  the  seven  additional  heavy  lines. 
I',i/ii/s.  —  W<'  have. 

This  will  give  tl'.c  result  wl.i.'h  is  seen  at  C,  less 
the  vertical  line. 

T,or/„r.  —  From  the  lower  end  of  the  upper  left- 


PIIAVTICAL   ItHslU.y. 


tlK» 


1  III  fiymnH'- 
ivill  givf  tlio 

1  mnrkn. 

at  ia  8<>t'n  at  h 
'  obliiiuc  liiif. 

<lraw  tlip  up- 
t'  uiiper  U'tt- 
liiri',  in  heavy 
ave  (hawn  it. 
we. 

at  h  in  H. 

viiiR  the  same 
he  (Iriiwii  ? 


■t unity  to  (;(>ii-      | 
yi't  certainly     : 

n  by  any  oiio 
art  of  putting 

inga  a  teai'hor 

il  heavy  linen. 
iciMi  at  C,  less 

rhe  upper  Ict't- 


hanil   litavv  line.  <lraw  a  verti.ai   liif   paralt-l   with 
til.' .lia'^onal  uf  tiie  ^'<lllal•e  ami   to   tli.-  .fiitiv   ol   the 
lieai-f.-it  scini-ilianieti-r.      ( )hsi'i\r  nie. 
l'i(jfl/s.  —  We  have  (liawii  it. 

Thin  will  K'ive  the  result  whieh  is  M-eii  al  <'. 

7',„„./, ,■/•.  — Mow   many   eoi-reMpoielin-^'    lines    <loe* 
Hyiiimetry  now  refpiire  to  he  (liawn/ 
f'liiiil's.  —  Seven. 
y,,,„./„.,-._l)raw  them,  aii.l  eras.-  the  loiistruetioii 

line.s. 

]>„f,i/s.  —  We  have,  and  it  >,Mves  us  a  cross. 

The  result  may  he  seen  at  A,  less  the  foiistruetioii 
lines.  It  is  a  simple  eomhination  of  straight  lines; 
but,  hecan.se  the  lines  are  .symnu'trieally  arranged 
about  a  eeiitre,  the  effect  is  pleasing. 

A  Kosette,  lUustratinK  Symmotrioal  Arrannement  about 
the  Centre  of  a  Square. 

Here,  at  D,  we  have 
another  simple  illustration 
of  the  prineiple  of  .symmetri- 
eal  arrangement  about  the 
centre  of  a  .sipiare.  The  form 
may  he  used  for  a  blackboard 
lesson  in  this  wise:  — 

Tfiir/ir,:  —  Draw  a  scpiare 
on  its  diameters  ;  adil  the  di- 
agonals.  Thns.  From  the 
upper  end  of  the  upper  left-hand  semi-diagonal, 
mark  ott'  one-eighth  of  its  length.  Thus.  What  does 
Bymni''try  now  recpiire? 

Fujjils. — That   the   same   length    be    KKirl^cd  otV 


10 


no 


'Ih.ti  Ums'   M.l.\(AL 


tVniii  .ii'li  I'lnl  »(  til''  «liii^,'i)iiiil,-<,     Wf  Imvo  iiiurkfti  it 

•'»V.  .     , 

Ti'iiohi')'.  —  Knnn  lit"  uii|u'r  t'lul  ot  tin-  vcrtiriil 
tliaiin'tcr.  m:irl»  "tV  ..n.-ci^'litli  of  tlu^  Ifiintli  of  itn 
lialt'.      riiiiM.     Wliiit  ilors  syiuniftr.v  in>w  rr(|iiin>? 

I'li/iHs. — 'I'lial  llif  Miini-  IfiiHtli  I"'  miirlu'il  olT 
\v»[n  catli  riid  <'l'  ilf  ih  ■•.in'tcrs. 

Ti'iu'lirr. — Oil  til"  uii|MT  niilc  of  tlic  iipiHT  li-ft- 
liainl  Miiiii-ilia^roiial.  an  a  liasc.  licj^iiiiiinK  at  tin-  jioint 
of  (livi>*ioti,  ai«l  ifrmiiiatiii^;  tit  tlin  ccntri'  of  tlio 
H(|iiarf.  iliaw  a  siin|ilc  curve.  TIiuh.  (Seen  at  '/ 
ill  v..) 

t'li/ilh. —  Wi'  liavr  tirawn  it. 
Ti'iiihi'i: —  Wliat  (loi'H  syiiiiiu'trv  now  rfmiirc? 
I'„f)i/s.  —  That  .M'Vi'ii  other  similar  liiifs  hi'  ilrawii, 
havinj,'  thi"  saim-  relation  to  the  I'l'iitrc  of  the  Mciuare. 
Tror/ii'i:-     Draw  thriii  acconlinnly. 

I'liiil/s.  —  We  liave.  (Seen  at 
/>  in  E,  h's8  the  short  eiirve.) 

Trurhi'i'. —  From  the  upper 
point  of  ilivisioii  on  the  vertical 
diameter,  draw  u  curve  fending 
from  the  diameter,  to  toiidi  tlio 
lirst  drawn  curve  a  litile  helnw 
itH  centre.  Tims.  (Seen  at  h  in 
K.)  What  does  symmetry  now 
require? 

/',tf,l/s.  —  Tliat  seven  otlier 
simihir  curves  in'  drawn  in  tlie 
.seven  corresponding  parts  of  the 
sipiare. 

IV'irlirr.  —  Draw  them  accord- 
ingly; then  draw  the  sides  of  the 
.s(piiire  in  lieavy  line,  and  erase 
the  diameters  and  diagonals. 


The   final   result   ia   shown   ;      D,  less   the   dotted 
lines. 


•o  nmrktMl  it 

till'    VITtii'llI 

I'liKtIi  of  itH 
ri'i|uin> '.' 
llllU'l<«'il    •'•1" 

'     ll|)|HT  li't't- 

nt  tilt*  ]Miint 
iitrt'  ot  tliH 
(Stu'ii    lit   '/ 


rciiiiiri'? 
fs  be  drawn, 
till-  s(|iiiiro. 

vv<«.  (Scfii  lit 
it  ciirvi',) 

11    tllf     llJipiT 

I  till"  vt'itiiiil 
mvt'  It'iiiliiiK 

to  tolH'll     tllK 

,  litilv  below 
(Sct'ii  lit  h  ill 
nunt'try  now 

seven  otlier 
Iriiwii  in  tlio 
l»  jmrts  of  tlie 

rtlu'niacfonl- 

le  sides  of  tlie 
lie,  and  eiiise 


iS    till!    dotted 


I'ltWrWAI.   ItKSlUS. 


Ill 


At  tinier*  i'ei|iiii-e  tile  ]>ii|iiis,  win  n  uoi'kin^  in   tliin 

Wliy,  to    llUlke    tlieir  Uliswers    iiilll|>lete    .Hlllh'llielits,  UH 

expliiineil  ill  tdiapter  two. 

I'niiii  the  illiistnitioiiH  wliiili  iiiive  now  lieen  >iiveii, 
it  will  lie  seen  tllilt  tlli'<  Jirineiple  ol' desi;,'!! — .xyniine- 
trieal  arraiif^enieKt  al'oiit  ti  ceiitrc  —  in  co  eiwily  eoiii- 
pndieiided  and  so  easily  ohserveil  in  piiictiie,  tliat  it 
can  l)e  taiifjlit  to  yonn^  cliildn  n  almost  at  tlic  outset 
of  tlieir  drawing;  career.  \'oii  will  often  llnd,  in 
(^ivin>{  IcHMons  from  tlic  Idaelihoard,  ax  just  illustrated, 
that  attention  paid  to  this  prineiple  will  greatly 
ahiid),'e  yoiir  lahor,  whih  the  pupils  will  niaiiifi'st  iii- 
ereased  delight  in  their  work.  Voii  will  often  llnd, 
nlso,  that  attention  paid  to  this  priiu-iph'  will  he  of 
servicH-  in  H'^''">?  dietation  lessons.  .\j,'aiii,  pupils, 
when  drawing  from  copies  on  the  cards,  will  he  },'reat- 
ly  helped  hy  a  ktiowledj^e  of  this  pri;ici|ih'  of  .symmet- 
rical arran^ji'ineiit.  .\  iK'sigii.  which  would  otherwi.se 
appear  to  them  intricate  and  ditliciilt  of  execution,  in 
tliscovered  to  he  (piiti!  tho  reverwo  when  vii>w«'d  in 
the  light  of  tliis  knowledge.  It  i.s  soon,  tliat  if  two  or 
three  ditVercnt  lines  can  he  drawn,  in  themselves  sim- 
ple, then  the  whole  design,  which  is  hut  a  coiiihina- 
tioii  of  these  two  or  three  liuew,  can  be  quite  us  readi- 
ly drawn.  Symmetry  is,  indeed,  the  ki'y  which 
unlocks  many  of  the  secrets  of  de.dgn  and  drawing. 

See  that  your  jiupils,  wlien  they  examine  the  draw- 
ings on  tlieir  slates,  do  not  look  at  them  ohiiipuly ; 
for,  if  they  look  at  them  thus,  the  drawings  are  di.s- 
torted,  and  tliey  fail  to  see  them  a.s  they  arc,  and  heiico 
cannot  tell  whether  they  are  correct  or  not.  The  eye 
iiiust  he  directly  opposite  the  (lentro  of  the  drawing. 


ih 


TKAL'IIKUs'   MAXIM. 


8rnim«trloftl  Arrannemant  about  th*  Oantr*  of  an    ffiquU 
UMral  Trlkiiile. 

liii<ti'U(l  of  II  Hi|tiari>  (or  tin* 
l^'i'oini'trii-al  lia^i^.  liikr.  tliM 
tiiiK*.  itii  i>)|iiiliilcral  tnah^l*-. 
Iliiving  limwii  tlic  tiiaii^'li', 
ImhccI  t'lirli  hIiIc;  t'l'nm  I'uili 
(loitit  ut'  hiHi'i'tiitii.  iliaw  it 
Htrai^lit  liiH'  to  tin-  opjio.-iti' 
aiinl"'.  Til*'  lii"''*  will  'roi*" 
cai'li  otliiT  at  tile  rtaiiii'  |Hiiht. 
jj- —  — till'  ci'iitrc  ol'  the  iriaiijjii'. 

This  will  nivi'  six  li^jiit  triunj;h's  Hyinnutiiiullv  ai- 
riinni'd  iiroiiml  tin-  cciitro  of  tin'  lar},M'  triangle  Coii- 
iH-ct  llif  iM'iitri's  of  till-  siili-<  of  tlic  nri;;iiial  tiiannlc 
liy  Htniinlit  liiu'w.      AiM    tin'    ciin-id  liiuH  as   at     I-'. 

^'oll  ininlit  stoji  lu'H',  fiT  till' 
<lf(*igii  is  syininctrii  ally  i><  r- 
fi'i't.  Take  aiiotliiT  stt'|i,  how- 
ever, iiiitl  udil  the  furvt'd  lines 
us  ut  (i ;  ulwo  the  outer 
strai^iht  lines  paralh-l  with 
the  inner  trianjjle.  Ilrase  the 
(l<>tte<l  lines.  Tim*  yoii  ol'tain 
u  new  <lesij,Mi.  Voii  iiii;,'ht,  in 
Q  a  similar  manner,  take  another 

sti'p,  uml  obtuin  a  thinl  design  ;  uml  so  on. 

Tills  ilhistrutes  whut  was  meant  when  it  \viu»  miid 
that  frei|iiently  an  elahorute  desi<,'n  eontuins  in  itself, 
niurkiii:,'  the  diileivnt  stup-s  of  its  growth,  .|nite  a 
numl'er  of  less  elahorute  designs,  which  are  reudily 
discovereil  l.v  aiialvsi:!.     Thu«.  the  design  at  G  <;on- 


- 

'« 

/'->'^ 

// 

, 

//■ 

'>C'' 

V 

A 

of  an   Bqiil* 

|uaii>  for  till' 
".  Ink).  tlii'« 
Till  tnaii^l)-. 
till'  triiiiiuli'. 
;  iViilM  t'lirll 
inn.    ilniw    Ik 

till-     OpIKwitl) 

■5    will    rriiKH 

Mitiiii'  |Hiiiit, 
till'  ti-iiiii^li'. 
iictiiiiill.v  ar- 
;iii;^li'.  Cmi- 
iiial  tiiaii^lc 
ics  UK  at  !■'. 
licrt',  I'cr  till' 
I'triiully  i>i'i- 
HT  Mtl'lP,  liow- 
!  curvi'il  liiH'H 
II  till'  iiiiti'i- 
parailrl  with 
I'.  i'!nisi'  till' 
111-^  yoiiolitiiiii 
rmi  iiii^lit,  ill 
.  taki'  aniitliiT 
III. 

II  it  Wiis  Kiiiii 
aiiis  in  itsrll'. 
iwtli,  i|uiti'  a 
1  an-  ri'iiilily 
;n  at  Cr  11)11- 


I'HACTHM,   /(A..s/»;.V. 


Il:i 


tiiiim  tint  mil'  at  I-',  wliili-  liirtliiT  aiiiily.^it  nmuiIiI  ili'<* 
I'loHi'  iitlnTH  roritaiiii'il  in  V, 

8ymni«trlo*l  ArranRflnient  about  th«  Uantra  of  *  Cirola. 

Draw  ariri:li'  on  it.-«  lioi'i/.i)n- 
tiil  ami  vertical  ilianii'ton* ; 
itilii  two  otluT  iliaini'ti'i'?<,  <!!• 
viilin^  till'  rirrlii  into  I'if^lit 
i'i|iial  (lartM.  Froni  rin'li  I'liij 
of  the  liori/.oiitui  ami  viTtii'iiI 
tiiaiin'tiTs,  mark  otV  nni'-si.xth 
partof a.Ht'nii-iliiinii)ti'r.  Start- 
ing from  till'  ii'ft-lianil  point 
of  tlivi-sion   on   tin-   liori/ontal  u. 

iliami'tiT,  ilraw  an  o),'i'i'  mrvi-,  trrniinalin;,'  in  tin' 
ri^lit-liamt  point  of  iliviHioii.  Ui'pritt  this  riirvi'  as 
nnmv  tiini's  ii«  ri'ipiin-il  liy  xynnnt'try.  .\<lil  tlir  fan- 
liki-  forniH  mi  tin'  otln'r  ilianiiliTx,  an  hi'i'Ii  at  If. 

If  you  ^ivi'  till'  fmni  at  II  nr  (i  an  a  lilarklioanl 
li'Hsmi.  ilraw  only  mii'  curvi'  at  a  tiini',  anil  li-t  tin'  pu- 
pil!* mid  tlu'  otIii'rH  ari'orilin^;  to  tin*  Itiw  of  symiiii'try. 
If  }'ou   j;ivi'  I'itliiT  as  a  ilirtiitioti   i'Xi'ri'i»c,  in  wliiiii 

casi'  you  can  easily  lix  ujion  tlii'  lui'aMiri'nii'nts.  pnn' 1 

in  a  similar  munnt'r,  ilirtatin<;  oni>  linr,  ami  ri'ipiirin^ 
till'  pupils  til  iiild  all  till'  rorri'spomlin^  lines. 

l''or  iitlii'r  t'xainpli's  of  synimi'friral  arranj^i'iiii'iit 
iiliout  till'  ri'iitri'  of  a  sipiai'r,  lirrli'.  lii'.\aj.;on.  pi'iita- 
f^on.  anil  trianj;l(',  si'o  tlii'  di'si^'iis  .\,  I'..  ('.  D,  K.  in 
till'  ui'xt  rliaptiT,  wlii-ri'  a  roiiM-ntional  Ifat  i>  tin' 
priin;ipal  I'leint'iit. 

From  tini"  to  tinii'  n-vii'W  llii'  piipiN  in  thr  pr.ini- 
pli's  explained  in  tlie  tirst  series  of  iupI-. 


w 


114 


rHAVIIKH/f  MA.St  AL 


ANfK    nK    I'AHT-. 

111..  II. xt  tliiiiK  i»  will  '»'  wfll  for  yon  to  tfiu'li  your 
{.tipil^  in  th.  ii»-uiiiii«  of  Hymmrtricttl  urrim^i'in.'iit 
on  tui  iixkthiit  Im,  on  it  .tniiulit  liio-.  Tlii*  ri'«|iiiri'» 
Liilun.'.-  of  imrtx.  — timt  tin-  rinlit  hulf  of  u  .If^Kn 

^1 1,1  Im.  Iikr  111.'  I.'fi.     Wli.ii  you  liiivo  >.yniiiM'tri.-Hl 

urruMKi'mt'iit  iilniut  u  .•.•iitn-.  any  ^.^rlli^{Ilt  liii.-  .Iiii«ii 
tliroiiK'li  till-  .•.•Mtn<  will  .livi.l.'  tli.-  «l.'xi«n  Into  \\\» 
•'.|iittl  |.intH,  wlii.li  will  alwiiy*  I..-  juMt  iilik.'.  \M. 
wli.'ii  you  liiivf  nyiinnftri.iil  urruiiK«'ii»''iit  ""  i"'  »""•• 
tlif  ilf-iKii  iiiu^t  111-  .livi.l.'.l  on  til.'  u.\i?'.  otlnTwino  tlio 
|mrt-<  will  !»•  mi-.|iml  nn.l  iinlik.'.  In  tin- lii^t  .■ui«-. 
if  til.-  HV"!  n.tii.iil  uiiunK.'ni.'nt  U  ul)out  tli.<  cftifro 

<.f  II  triun«l.-,  tli.n  ii  liiu-  < Iriiwn  inuHt  bo  tliri.o 

or  »'\\  tini.'.-.  .Iriiwn  ;  if  iil'out  ill.-  .•.■iitr.'  -.f  ii  H.|imiv,  it 
niii^t  1m-  f.Mir  ..I-  .'iKlit  tiin.r-  .Iruwii  ;  if  alHuit  tin-  n-ii- 
Iri-  of  II  iM'iilii^jon.  it  iniiHt  l.f  liv.-  .>r  l.-n  tiiiifn  .Iniwii ; 
if  aliout  tln'.vntiiM.f  iiriirl.s  it  must  1..'  .Iniwn  iw 
niiiny  lim.'sus  tli"  .iirl.-  .un  Im-  aivi.l.'.l  into  partH. 
Ilk.,  "til..  ..11..  in  wlii.li  111.-  llrM  lint'  of  tli.-  kIv.-ii  kin.l 
iH.'mwii.  IJut  ill  tin-  m.'.oii.I  .•an.',  wln-u  a  lim-  lia-* 
1m...|i  on....  .iiawn.  it  .an  only  I"'  'Iniwii  a  Mv..n.l  lim.., 
till!  Hf.'onil  lint'  luilaii.iiiK  tin-  lir^*!- 

'I'll.'  larK'f  I'iU't  "f  •'"•  «'X''»'<'i'«»''<  i'»  t'lf  "''••"H'l  i**'""''"* 
of  iimlH  illnHtrat.'  f-yinno'tri.'.il  arniii«.'ni.'nt  on  mi 
uxi^.  Ka.li  .'f  til.-  l.u.U,  f.if..xain|.l.-,  at  l>,  in  Kx.T.'is.- 
I.,  s.Ton.l  s..ri..s.  i^  syiiiin..tri.ally  ;.iTanK'<l  on  tli."  v.-r- 
tical  .Iiaiinl..r  .>f  lln-  Hl'ian-  wlii.li  ..n.loM..K  it.  Ol.- 
M-m-  that  tliiH  liiM-  alon..  will  .livi.l.^  tlu'  I'U.l  into  two 
,.,|nal  partn;  not  ho  with  th.'  ros..tt..^  at  ,i,  in  tin' 
Ham.'  .'Xi'ii^is...      1  n  Kxi-r.-iiii'  II..  ><''on.l  MTii-x.  we  hav 


"1 


ASf8.  — MAI.- 

ti)  ti'ui'li  your 
urruiii;)'in<>iit 
'I'IiIm  ri'i|iiir)'M 
I'  <)|'  It  <li'><i«n 
i>  nyiiiiin'triiul 
It  line  ilrii«u 
*\\iu  into  Iwii 
t  iiliki>.  Kilt 
it  on  nil  nxiM, 

iillliTwiHO  till' 

the  tiint  <'i(.«f, 
lilt  tilt'  rt'iitrii 
iiiMt  1«>  thrill' 

1(1"  11  HI|lllU't',  it 

iiImiiiI  till'  n-ii- 
tiiiii'H  ilmwii ; 
he  ilniwii  ii!4 
li'il  iiitii  |iartH, 
Ik-  ^ivfii  kiml 
I'll  li  line  liii^ 
11  M't'iiiul  tiiiii', 

0  Hocniid  Hi'rit'H 
Hi'ini'iit  on  uii 
;  /<,  in  KxtTi'is.' 
pil  on  till'  vrr- 
ilnst'H  it.  «>i>- 
II'  luul  into  two 
s  lit  (f,  in  till' 
srrii-s,  w»'  liiivi' 


I'N.irrn  it.  in>:>mx 


IIA 


It  U'lod  ilhi«tniti'>!i  of  j-vniiiii'triiiil  iirriin^ji'iHi-nt  oit  nv. 
HHin.  I'oitihiiM'il  witli  MyiiiiiM'lrii'iil  itrritn^i'iiii'iil  itlMiiit 
H  ri'niri'.  Hin'li  Mi'|)itriiti<  ImhI  Im  Myiniiti'lriiiilly  iir- 
ntiiKi'il  oil  nil  itxii :  utiito  tlir  ilini^n,  t'ciii>it|i<ri'ii  n*  u 
wlioh',  in  Hyiiiiiiili*ii'iilly  iirriin;;i"l  iilMiiit  it  ifiirn, 

UKi'KtiTiiiv,  imm/iiNTAr.  asu  skhtum,. 
Wlii'n  yoii  liitvc  iiiitili'  It  ili'-ij;!!  iiljiT  till'  niiiniM'r 

of  tlloMC  Wif  IlllVl'  I II  i'illli.ii|i|iln{,  yoll  (1111,   for  IlllillV 

I  |>r.ii'tii'iti  iiiirpoNrH,  titki-  tin-  iti'xiitit  mt  »  unit,  uml  ri" 
(  |)i'.it  it  all  iiiili'llniti'  iimitlti'i'  of  tiiiirx.  I'itlo'r  in  ii  liori- 
I  iioiititl  or  ill  It  viTtiriil  ilirt'i'lioii.  Tliii*  it  iloin-  in 
itri'liiti'i'tiiral  ilt'i'orittion,  In  tlii'  ili'siKH)«  fur  i'iir|MtK. 
Hiiij  all  kiiiilN  of  oriiaiiH'nti'il  ti'Xtili-  faliricM,  ami  in 
I'ltvi-rinn  MnCaii'H  yi'iiiTally.  Ofti'ii  a  fi'W  lini'H  uri- 
aidliil  for  till'  |Mir|ioMi'  of  iinitiii^  tin-  ri'pititioni  of  tin- 
ori^iniil  unit.  Sonii>tinii'H  ilir  unit  itm-lf  may  liaM- 
liltli'  or  no  licjiiity:  yit.  if  ri'iii-ati'il  virticaliy  or  lior- 
izoiitallv,  till'  n-milt  iiiroincH  viTy  |)li'a."tin>;.  Kxinj.r 
(.,  MtHHiml HfrifH,  iliiiHtruti'Mliorizontal  ri'iii'iition;  wliilo 
KxiTrii*!'  v.,  Nitinn  m-ritm,  illuKtrati'M  vi-rtii'iil  ri'|it'tifiiin. 

riKI'OMK    AVI>    MUKAinil. 

Wlii'H  tim  vyf  I'iiIIh  iipon  a  ilf»*i><n.  itml  in  I'linti-nt 
to  ri'iiiiiiri  wIhti"  it  falls,  tliat  iiiiiility  in  tin-  ili'fi>,'n 
wliicli  proiliiics  tlii.-  ijiiii'tiii;,',  a),'rii'alili'  I'llV-it.  ii*  ilf- 
nomimitcil  njiom'.  \f  flicn-  i*  it  lark  of  rt'ixwf.  tlim 
till'  I'yi-  fi'i'ls  iiii|K'lli'i|  to  wiimlrr  ovi'r  till'  iii'«i;{n.  or 
olf  it.  fimliiit,'  no  ivst.  'I'ln-  .■^I'lisation  ih  ilrcidi'illy 
iiiii'omfortaMi'.  Tims  tlii'i'i'  is  no  vvs\  for  tlir  i-m- 
wlii'ii  looking  u|ioti  a  I'lirpi't  wliich  Iium  only  >.traij,'lit. 
Iiaralli'I  liiu's;   l.iit  it  litis  im|ii'l|t'(l  to  follow  llir  IIih'm 


Ittt 


IKAVHUNif   M.iSfAl.. 


Iiltln*r  i»Ht1  »1ii!l>««r  ai •^»•»  'J***  t*nm\  fntfocfari'  irth»»r 
Rlrnitflit  lii»-i«  i!r.tMiiiK  iIm'  rtr»».  ni«l  liif  wiui  U'riiiK 
|iii.|.'iit  y  '*(  »*»'•  ••>■••  I"  •lli»li»l"l>"''  *'•  '•i»»»"»'l  "1 
|.urull.  I  "triiinht  lim-*,  'li.'  .I<  •inn  ••.Mi«w!*  .mly  ..f  .011. 
.•.•iitri.'  .ir.  I.'",  tli.i-  ilx'  t  •  '  '"y  »(  th"  lyn  i*  i'» 
inov.'  r..tiii.l  iunl  r.Miii.l,  loiloAiiiu  tli.'  .in'lM*.     TliU 

t |i.h.y  i- .limliii.lM'il,  or  miM-  iilto«i'tl»'r,  wIm-ii  lli- 

.  ir>  li*  i»r<'  iri»»n<l  \>y  u  lf«  ttruinlit  lim-. 

rn  ..r.l<'r.  llu-ii,   llii»t   u  tUmi«ii   muy   Imv.-   r.'p.>».'. 

tlii-rf  inii«»  I"'  HO  l"MK,  iiiiii>t<'rrn|ttiil  liin'*  i piU""- 

tivi'ly  loii«  lor  ihf  i»i««'  of  tli.«  .l.'»i«iii.  •itlur  ..triii«lii 

I     or  .iirvnl  i  iHif  tli.'iv  niiiHt  Im-  u  .Im- I.iiiiitioii  ..» 

liiM'",   ctmiKlit   uii'l    .iirv.-.l.  v.rti.ul.  Iion/oiilul.  uihI 
ol.lii|ii«.     Willi.'  .iff.'mptiiiK,  how.'vi-r.  lo  Mtxm  n*- 

i     |»o»i',  uvoiil  ail  iiii.lii''  iiiiiltii»liiiiti.Mi  »(  \U\f*;  \'«t  ti<*> 

'  iiiiiiiy  liiif^  toiiCiiM'  iiiitl  ilt'.lioy  tin-  ftVi'il.  Mfi',  »•»•■ 
lliiir  llii-n-  arc  "oiim'  liin*  '"•i.li  niort'  pioiiiiin'iit  llnih 

I  otlii'ri*,  —  ntort'  proiiiiiK-iit  l.y  rriiwoii  ol'  tlnir  I'lintli. 
uiiil  not  of  llfir  n\/.,:  ul  llii*  ^Hi«.'  of  .lrawiii«;  I'or.  if 
l|„.ri.  Ill- It  Mi.liliiifM,  iIk' 'I'^i^ii  will  la.U  i.r.'u.llli. 

j     —it  wiP  not  pli'iiM-  lit  till-  lirnt  Kluiu-f.  uiiU  m>  will  ii"t 

*       lliviti-    flirflllT    illHlMTtioll,    lloWrVtT    IIUl'll     ii*    'I'-tllll- 

!     ininlit  iilfiiM'  wlii'ii  iivi'i'fnlly  "tuilif'l. 

l'mNlMI'l.i:!»    (IK    DKHIUN    liKltlVKIl    KUOM    NATI   IH^. 

\         'r'ti'  ).tint'iiili'-  of  iiriifti.iil  ili'MKii  ari"  ili-rivi'il  liom 

!     tt  «iua>    ol"  luituiv,  .•Kpr.iiilly   fioii    u    Mtii.ly    of  tli.' 

i     VK.:,.tai.li.       .rl.l,  — of  lliirt-ern,  frultit,  l.-ttVfK.  vim-. 

WhiMi  WM  .■xtiiiiiiii'  flowi'i-K.  w.'  tlii'l  th.'ir  pi-tulH  hvui- 

m.'tri.iilly  iu.iiiiK«'«l  iiliout  .fiitriH  ;  wliili- I'luli  p'tal. 

.•oiiHi.lir.".!  liy  itH.'lf,  ix  Kyiinii.-tri.nlly  urniiiK.-il  on  an 

iixiH,     WIh-11  wi'  oxuuiiiif  I.-uv.'h,  wi-  liiul  tliut  <ii'  1"  i" 


I^HVrirAI.  nUHlUS, 


IIT 


ir.  iiixti'tui  itf 

'-t  only  of  riMi- 
till*   I'V"'   ••  ''• 

il»>r,  wIm'H  iIm' 

I'M. 

lirtvt-  rt»|M»i'. 
\\\%>*  ii-iiiii|iiiru' 

iitlii'c  i.truinlii 

iiiiiiiiiiiiiii)it  <>r 

iitn/Diitikl,  itml 
til  Mfi'iirM  ri'- 
line* ;  fiif  t'Mt 

I'lM'l.  Sfl',  Inn. 
llUllliltl'tit   lIllMI 

I'  tlicir  liii«ili. 
Iinwiii^:'.  I'i>r.  it' 
I   lu.'U  l>ri'ai|llt. 

Ihll     il>t     lli-tuil" 


ItOM    X ATI  UK. 

ic  (lirivi'fl  Iritiii 
\  Ntinly  of  till 
.  Ifiivf".  villi". 
ifir  pctiilK  nym- 
liilf  cii'li  I»tal. 
urriiiiK<'<l  "II  "II 
iiiil  tliut  »'ii<li  i" 


t. 


.ytlMVM'tHi'illly  iirniiiU'tl  "M  nil  i»^i".  »*Jii"'lt  i*  •'••'  "liil- 
rili  ill  li'uvi'it  litiviiiu  II  «iiitfl>'  lol"'.  'riii*.  of  I'tttiwi'.  i* 
imJy  tw«»  iif  til"  K"'i"*rttl  f^nn  <»l"  iln'  l»*(»f.  ••••!  "►!'  i»« 

tli'fdlU.  Tliiii.  ••«>.  'Ill  <Hru«i<<iiul  l«i»f  viiilntf*.  ill  U 
timr*-  <|i'<  itir.l  iiitiitiM  r.  tin'  law  nf  nymiiirtritul  ili-vil.Hf 

IIH'llt,  W*  <|iM'«  till'  l'llll-lfl»r.  with  its  l>llli<|ll«'  liuw,  wliili* 

MMiu*  ti<twt>rit  iiri>  Ml  irn-Kiilur  llii-yi'iiiiiMit  Ih<  iluaitilii'^l, 
ittul  III'',  tlitf  rori',  'Hllfl  iiin'iiiiil'iii*.  IihI'-i'iI.  imtiirM 
iiKiK  itll  IWriiiKi  I'Ut,  wliili'  xln'  'I'M'*  tliix,  xlif  p«liim>t  A 
iliH'iilcil  |)n>fi'ri'iii')'  f'lr  tin-  i«yiiiiiii'tririil. 

Till'  luw  III'  nviiiiiiitriral  (li'V>lit|iiiii'iit  on  itti  uxi"* 
ImliU  I  nil',  ill  ili«'  iiiuiii,  of  uiiiiiuil  loriiiK.  'I'liii' tlii< 
liMiiiitii  11^111"  t'ointi^tit  III'  two  )'i|iiul.  Miiiiilur  imrtn.  tlio 
ohi*  liuliiiH'inu  till'  otlnr. 

Wliut  \n  tiiH'  of  tlMMi-  iiifMliictM  of  niitiir'  tliiit  tiiii 
III'  Bliiilii'il  liy  till'  iiiiiiiili'il  lyr,  in  foiiiiil  to  !..■  i.||iiiiily 
trill'  of  till'  iiiii-riioropir  worlil.  KxiimiiH'  •iiow-tli»ki'» 
iniili'i' Ik  iiiii'roi«i«i|ii- ;  the  rryitiiU  i-xliiMt  u  urviit  vu- 
rii'fy 'if  ••liiiriiiiin{  roriiii* ;  yi't  I'urh  ip»  »yiiiiiii'irira!ly 
iirriiiiKi'il,  uliiiowt  with  Ki'omitririil  pri'iiHioii,  uhoiit  ii 
ri'titri'. 

Ill  ilinfriliiitiiiy  lii-r  lint"*  of  >{rowfIi.  iiafiiri'  i^  alw» 
olmi'ivaiit  of  lni'iullli  ami  ii'poKi'.  Kxaiiiiin'  th''  "tiiu- 
tiiri"  of  II  h'lif.  ThiTt!  uri'  thi'  rilm.  or  only  u  niiiliili, 
UH  till' i'U«t' muy  hi'.  Mtroiiyly  il'-lliifil ;  tlnn  ronii'  tlir 
vi'iiiM.  h'HN  HtnniKly  ili'llin'«l.  itml  tivl<iii«  a  ililh  nnt 
iliivttioii ;  ti'iil  tlii'ii  a  liirtluT  «iih(livi»iiiii  of  tin-  >iiir- 
fill''  l>y  vi'iiih'tH,  ami  i-vitii  IIiht  triwinKH.     What  iM 

trill'   of   till'    ii'af.    it    tri f   tin'    tr it   a   wli'.h'. 

Stiiiiiliii«  I'l'iii'utli  thi'  tri'i>.  ami  InokiiiK  "p.  wi'  hi'hold 
tin-  lai'Hi'  iiramhi'M  intowhifh  tlm  trunk  iliviih'H;  tlii'ii 
follow   thi'    minor  MuhdiviMioiit.   ilowii    to  twi^M   ami 


nx 


TKACIIKliS'   MANUAL. 


leavi'M:  tliis  is  ii  coinltiiiivtioii  wliich  givos  at  omc 
bri'iidth  as  tlic  rcstilt  of  tlm  gi-iicral  fcaiuri's.  and 
rojiosi  as  tlio  rt'sult  of  the  aiMcd  iniiior  IVaturt's, 
All  is  harmoiiioiis  ami  agrt'i'al)lt'. 

Rcijuirc  your  pupils  to  hring  into  school  Icavi's, 
flowers,  sliclls,  insects,  tliat  tlii'ir  ibrnis  may  l>e 
stiulieil  in  connection  with  the  lessons  in  tlrawintJ. 
Require  them  to  bring  tin)  greatest  variety  possil)le, 
not  only  to  be  eomiiared  with  one  another,  Itut  to  bo 
drawn  rapidly.  The  study  of  art  and  the  study  of 
nature  will  thus  go  hand  in  hand,  ai\d  each  will  help 
the  other.  When  there  is  an  intimate  c  .nneetion  be- 
tween two  things,  they  can  both  be  learned  together, 
as  easily  as  either  can  be  learned  alone,  and  often- 
times with  less  eft'ort. 


OKIfJINAF,    DKSKi.V.S    »Y    TlIK    I'UPIL.S. 

Guided  by  the  principles  which  have  now  been  ex- 
plained, the  [)upils  will  be  able  to  construct  original 
geometrical  designs,  with  both  I'ase  and  understand- 
ing. They  should  be  permitted,  therefore  (for  hard- 
ly more  than  permission  will  be,  necessary),  to 
exercise  their  inventive  powers  in  this  manner. 
They  can  use  the  construction  lines  employed  in  the 
copies,  anil  dr.iw  upon  these,  as  a  basis,  lines  wliich 
will  give  new  combinations ;  or  they  can  modiiy  the 
construction  lines  themselves,  by  dividing  them  differ- 
ently, or  by  adding  new  ones.  In  devising  their  new 
geometrical  designs,  they  will  be  limited  by  the  al- 
phabet of  lines,  straight  and  curved :  they  will  have 
nothing  to  do  with  natural  forms,  except  to  follow  the 
general  principles  deduced   from   a   study   of  these 


.- 


givi's  ivt  oiii'o 
tViit.iu'es,  anil 
iiior    I'ciiturf.s, 

HcllOol    1('IVV»'S, 

)ri)is  iniiy  !>•' 
;  ill  tlrawiiig. 
riety  possililc, 
lu;r,  Itut  to  1)0 
the  study  of 
L'licli  will  liclp 
CJimcction  be- 
riuitl  togotluT, 
:ie,  iviul  oftt'ii- 


uriLH. 

now  l)ef  n  ox- 
itnit't  original 
il  uiidcrstand- 
forc  (tor  Imrd- 
noncssary),  to 
tlii.s  niannor. 
iploycd  in  the 
is,  lini's  svliicli 
an  niodiiy  tlin 
ig  tliom  diffcr- 
sing  their  nt-w 
ed  by  the  al- 
thoy  will  have 
it  to  follow  the 
tudy   of  these 


PRAVTWAh  ltt:swy. 


11» 


forms.  Farther  idoiig,  tlie  direct  use  to  be  made  of 
these  forms  in  iiraetical  design  will  be  explained  and 
illustrated. 

Ins|iect  the  designs  originated  by  the  pupils:  eriti- 
eise  kindly;  commend  whenever  ynu  can.  Do  nnt 
judge  their  productions  by  a  high  standard.  Too 
many  lines  will  be,  perhai)s.  their  greatest  defect 
at  lirst.  destroying  the  breadth  of  the  design. 

With  the  hints  here  given,  teachers  can  make  the 
succeeding  exercises  very  agreeable  work  for  their  pu- 
pils. When  drawing  is  taught,  not  simply  as  an  ex- 
ercise of  copying  forms,  but  as  suggested  in  this  chap- 
ter, it  becomes  an  exercise  which  cultivates,  in  a 
wonderful  degree,  tlie  observing  and  inventive  powers 
on  the  one  hand,"while  it  imparts  skill  in  the  visible 
expression  of  knowledge  on  th<!  other. 

(!ard-Exeuci8E  I. 
Horizontal  Kepetition.  —  Bosette»  aod  Buds. 

FoKM  a.  — Draw  two  squares 
touching  each  other  horizontally. 
Draw  the  diameters  and  diago- 
nals ;  divide  the  diagonals  into 
six  equal  parts.  On  the  diame- 
ters, drasv  compound  curves 
passing  through  the  centres  of 
the  squares;  add  the  leaflets 
which  terminate  at  the  outer 
points  of  <livision  on  the  diagonals. 

Form  //.  — Draw  two  squares  as  in  the  last.      Draw 
their  diagonals  and   vertical    diameters;  divide   the 


12(» 


TKA  CUE  Its '  J/.l  A'  UA  L. 


upper  liiilvcs  of  tlic  tortiicr,  add  the  low<!r  lialvos  of 
till'  latter,  into  tliirds.  From  tlie  upper  j)()ints  of 
division  on  tin'  diajjonals,  draw  curvoa  tlirouj^li  tlm 
lower  points  of  division  on  tlie  diameters.  Finish  us 
indicated. 

Variations.  —  Make  a  horizontal  moulding  com-     I 
posed  of  alternate   sijuares  of  n  and  b,  —  a  rosette,     ' 
(lien    a    liuil.  —  and    not    less   than    three   of    each. 
.\gain.  make  a  vertical  moulding  by  repeating  a  sin- 
gle square  anil  bud  of  h. 


Oard-Exkkcimk  II. 

Buds  repeated  around  a  Centre. 

Draw  two  straight  lines, 
one  vertical,  the  otlu>r  horizon- 
tal, bisecting  each  other.  Di- 
vide each  into  si.\  e<pial  parts. 
Through  the  inner  [loints  of 
division,  draw  two  horizontal 
and  two  vertical  lines  of  the 
same  length  as  the  first. 
Fnite  the  ends  of  these  linos 
l>y  two  horizontal  and  two  vi'r- 
tical  liiu's,  thus  forming  live  eijual  sijuares.  Draw 
the  diagonals  of  the  four  outer  scjuares,  indicating 
the  position  of  the  leaves  of  the  buds  to  be  drawn. 
On  each  diameter  of  the  inner  square,  draw  two  com- 
j)0und  curves,  and.  in  ea<li  of  the  other  squares,  draw 
a  bud  similar  to  //  ii;  the  last  exercise. 


lowt-T  liiilvos  of 
ipptT  jioints  (»f 
BH  through  tlio 
ors.     FiiiiHh  aH 


luouhliii):;  com-  I 
b,  —  II  rosette,  | 
three  of  each, 
•ciieating  a  sin- 


tre. 

Btraiglit  lines, 
'  other  liorizon- 
ili  other.  ])i- 
ix  e(]ual  parts, 
iner  points  of 
two  horizontal 
il  lines  of  the 
as  the  first, 
of  these  linos 
al  and  two  ver- 
Kjuares.  l^raw 
res,  indieating 
\  to  be  drawn, 
draw  two  eoin- 
r  squares,  draw 


I 


I'HAVTK^M  liKsmS'. 


ll'l 


(".\i!i)-KxKi!<'isi:  iil. 
Coffee-Pot. 
Driiw  the  central  vertical  line,  and  diviile  it  into 
fourths;  add  the  other  vertical 
lines,  nialiing  tlie  width  of  the 
oblong  e(^ual  to  one-half  of  its 
height.  Through  the  centre 
of  the  upper  fourth  of  the  ver- 
tical line  and  extending  the 
same  distance  on  each  side, 
draw  a  horizontal  line,  for  the 
top  of  the  <'ort('e-pot,  equal  to 
one-half  of  the  width  of  the 
oblong.  Draw  the  outline  of  the  colVee-pot  and  its  lid, 
.\dd  the  spout  and  handle.  The  lower  band  covers 
one-fourth  of  the  lower  fourth  uf  the  central  line. 
The  other  bands  are  one-half  as  wide.      Finish. 

C.VItU-KXKUCISK    IV. 

Cup  and  Saucer,  Salver,  and  Muffln-Bish. 

KoKM  a.  —  For  the  cup  and 
saucer,  draw  a  vertical  line, 
and  divide  it  into  thirds. 
Through  the  lower  point  of 
division,  draw  a  horizontal  line, 
and  another  immediatelj'  below, 
twice  as  long  as  the  vertical 
line.  For  the  top  of  the  cuj) 
(not  including  the  handle), 
draw  a  horizontal  line  one-third 
longer  than  the  vertical  line.     Finish. 


11 


1'2'2 


TKAVIIKHS'   MAyiAL 


FonM  //.  —  For  tlio  Hiilvcr,  dniw  ii  vortical  lino  and 
halve  it.  Makt-  I  U  tliricf  an  loiij;  as  tlit<  vortical  lino. 
Draw  tlio  li)n«  curve  i)f  the  bowl  tlirouj^li  tho  centro 
of  the  lower  half  of  tho  vertical  lino  ;  aiM  tho  handles 
ainl  the  hase. 

^\uiM  i:  —  For  the  iiuiflin-disli,  draw  a  vertical 
line,  and  dividi;  it  into  four  e(|ual  parts.  Mako  1  2 
twice  tho  vertical  lino.  Tho  hamllo  oniupies  tho 
upper  fourth  of  tho  vertical  line.  The  howl  of  tho 
cover  is  a  weuii-ellipse,  its  width  rather  luoro  than 
twice  its  hei^?ht.     Finish. 

Variations.  —  Change  proportions  and  curvoH. 
Thus,  make  the  outline  of  tho  saucer  in  n  a  com- 
pound instead  of  a  simple  curve.  Modify  tho  .sal- 
ver by  making  1  -'  five  times  tho  vertical  lino, 
changing  nothing  else. 


Cakd-Exkrclse  V. 

VKKTICAI.    ItKl'ETlTION. 
Ou'Uoche.    Iipovps  and  Berries,  Conventionalized. 

FoHM  ".  —  On  a  vertical  cen- 
tral line,  draw  three  .scjuares 
touching  each  other.  Draw  the 
diagonals  of  each  sfjuaro  to  find 
the  centre.  Around  each  cen- 
tre, draw  a  circle,  with  a  diame- 
ter equal  to  one-third  of  the 
diameter  of  tho  square.    Arotnid 

these    three   circles   draw    the 

endless   curved   hand.     The   dotted   lines   show   tho 


r 


VliAfTlCAI.    l>i:Hl<iS, 


]-j;; 


cat  lino  nu<l 

vortical  lim-. 

I  tlio  ccntro 

tiu)  liandlori 

{  a  vertical 
iVrako  I  2 
iccupics  tho 
bowl  of  till' 
'  iiiui'u   than 


and  curves, 
in  <i  a  coin- 
lity  the  sal- 
crtieal    line, 


tlonalized. 

I  vertical  cen- 
lireo  s<]uares 
r.  Draw  tho 
square  to  find 
nd  each  cen- 
rtith  a  dianio- 
'-third  of  tho 
laro.  Arotnid 
es  draw  tho 
les   show    the 


jiarts  whicli  are  overIapi>ed.  'I'lu'  »«trai>,'lit  liiicf*  vixi- 
lile  in  till  iunnin<,'  pattern  are  drawn  on  the  dia^'mials 
"f  the  s(iuare»,      Kraso  the  dotted  lines. 

'I'hiH  is  a  sanip'e  o'"  the  miillnche.  an  orininiental 
form  which  was  used  hy  thi  very  earliest  historic  na- 
(i,,im,  —  us  l»y  the  Assyrians,  for  instanc".  Its  pe- 
culiar feature  c<uisists  in  the  windinj,'  and  interlacing 
of  the  loiijr  cui-ves  ahout  the  circles.  This  lieinj,'  an 
historical  ornament,  and  frc(|iiently  used  now.  pupils 
should  practise  drawing  it  until  they  can  readily  re- 
prcduce  it  from  i;;oinory. 

FoHM  h.  — Draw  three  squares,  as  in  figure  -.  ujion 
tho  central  vertii^al  line ;  then  the  loii^'  curves,  form- 
ing tho  outline  of  the  repeated  leaf.  Divide  the 
central  line  of  each  square  into  two  eipial  parts,  which 
will  give  the  points  on  it  from  which  to  draw  the 
smaller  curves  at  the  hase  of  the  leaves.  Tho  hase 
of  a  leaf  is  tho  part  next  tho  stem.  Draw  tho  circles 
lo  (ill  uj)  the  spaces  left,  and  the  stem  upon  which 
leaves  and  berries  are  supposed  to  be  growing. 

The  pupils  .should  now  be  able  to  draw  quite  rap- 
idly, and  at  tho  same  time  make  their  lines  much 
bettor  than  they  did  at  tirst.  See  that  their  pencils 
are  always  long  and  well  pointed,  otherwise  much 
time  will  he  wasted  in  attempting  to  make  proper 
linos,  [iideed,  you  must  economize  time  in  e\ery 
way.  Some  teachers  consume  tenfold  more  time  than 
do  others  in  getting  ready  for  recitations,  simply 
becau.se  they  have  no  system.  A  class  of  forty  pupils 
should  not  be  more  than  imo  minute  getting  ready 
for  a  drawing-lesson,  even  if  all  the  shites  and  pencils 
have  to  be  distributed  from  the  teacher's  desk. 


t.i4 


TK.IVIIKKS'   M.IMAL 


cxrrcist'. 
FoltM 


Cahi»-Kxkk»isk  VI. 

Ilnltl/ONTAI.    KKI'KTITION. 

Oullloche.     Leaveii  »nd  Berrien,  Oonventionklized. 

FiiKM  II,  —  Draw  live 
sqimroa,  tourliing  oni'  iiiiotlior 
horizoiitivlly.  Kill  tlifin  witli 
lui  niullcss  Imiid,  as  n,  in  tlif 
la«t  canl-t'xcrcisi!,  was  lillcd. 
Add  the  jtaralU'l  sidc-iini's. 

FoKM  /'.  —  I )r!i\v  live  sipiarPH. 

toiK'liiiijj;    t'ucli    otliiT  luiri/.Dii- 

tally.     Fill  tliom  with  rt'pi'iitcd 

loaves  lilui  tliosc  in  A,  last  card- 

\«ld  tlu'  parallel  side-lines. 

Draw  three  squares,  toiiehinn   liori/mi- 

tally.  A(hl  their  vortieal  diameters,  as  construction 
lines,  and  then  fill  the  squares  with  ropuuted  flowers, 
as  shown  in  the  copy. 

Caup-Kxkkcisk  VII. 
Simple  and  Compound  Abstract  Curves,  Balanced. 

The  curves  ;{  L',  and  H.'.  those 
which  end  nearest  1,  and  the 
spirals  at  tlie  hottoni.  are  all 
compound.  The  other  two  pairs 
are  simple  curves.  Kemeniher 
this  when  drawjuj;  the  curves. 

Draw  1  2,  and  divide  it  into 

four  equal  parts.     Alake  .">  I,  "» <>, 

^^^^—-^^^^^  Pqi'fll    to    three-fourths  oi     1    li. 

TnHTtir^^th^n^i-'^t  curves  .'J  li,  4  '2,  balancing  them 


: 

! 


I'HACIICAL  l)h:si(/X. 


\Jt 


mtlonkliaed. 
-  Draw  Hvt' 
J  one  '.inotlier 
ill  tlii'in  witli 
1,  as  II,  ill  tilt' 
^^l,   wiirt    lillfil. 

sidu-liiu'H. 
i\v  livi'siiiiart's. 
utliiT  liorizDii- 
1  with  n'jM'ivtcd 

in  /),  last  ciird- 

jliiiiK   lioriziMi- 
>8  construction 

JCUtlMl   tlowiTs. 


la,  Balanced. 

,  and  42.  those 
.'st  1,  and  the 
lottoni.  art!  all 
otht-r  two  iiaiV' 
•s.  KcniundxT 
\\f  tht'curvi'.s. 
divide  it  into 
Afak.- .'M,  n  (), 
burths  oi  1  li. 
balunLinf;  them 


! 


••.|ually  on  rach  sidf  of  tin-  v.-rti.al  lim-.  Draw  l»u' 
ninipit'  iiirvt's  nprinKinn  from  r>  and  Oto  join  tin-  cnrvt'it 
(ir«t  drawn.  Divide  1  I'i  into  four  I'ijual  part:*.  hIi-o 
I  -l.  From  thi-  central  points  t.f  division,  draw  tin- 
simple  curves  to  the  eentre  of  the  vert  leal  line;  and. 
from  the  points  of  division  neiirest  t.  draw  tin-  tulip- 
shaped  eurves  terminating'  at  the  lowest  point  ..f  di- 
vision on  the  vertical  line.  Draw  the  spirals,  with 
their  ends  joining;  the  ends  of  a  liori/.nntal  line  drawn 
two-thirds  of  Olio  p'Uft  of  the  vertical  line  ahove  'J. 
See  tliivt  all  the  lines  run  gracefully  into  one  another. 


<'AUI>K.\KKniSK  VIM. 
Simple  and  Oom;<ouiid  Abstract  Our»eB,  Balanced. 
It  will  be  seen  that  this  is  a 
Mlij,'lit  variation  of  the  last  ex- 
ercise, the  spirals  heiiijj  ilrawn 
near  the  centre  ^A'  the  vertical 
line,  and  the  long  coiniwniid 
curves,  terminating  near  1,  be- 
ing drawn  from  the  bottom  of 
the  ver»^ical  line.  Draw,  first. 
the  lines  on  the  left,  and  then 
those  on  the  right  to  balance. 

TIIK    Sl'IIJAI,. 

There  are  two  varieties  of  the  compound  curve 
called  the  spiral.  In  the  lirst  variety,  the  distance 
between  the  dirt'crent  spires  is  the  same,  as  shmvii 
at  I.      This   is  called   the   e(|Uai>le   spiral,  because    its 


I-Jll 


ruAvnimti'  n axial 


1 


l.rfiulili  iii'ii'iixfi*  Jihiriirinly  with  i>iuh  rt'Vcliifion  :  if 
in  uUo  iiillcil  till'  All  liimi<lriiii  »|iii'al.  fMiii  ii  <iii'(k 
niatlii'iiiiitii'iiiii  wlm  livcil  inui-i-  tliiin  two  iIhiiimiimI 
.VfiirM  an<>,  ami  wiw  llic  llrM  to  tl.-lim-  itK  iliamrtiT* 
iwiirft. 

It"  all  u|iri;,'lit  lyliinliT,   or   tin-    roimd    trmiU    of  a 
tree,  III-  woiiinl  witli  a  niiiuli'  laytT  of  roril.  ami,  it  a 

|ii'iNoii  llicfi  take  lioM  of  till-  t'liil  of  III il,  ami  iiii- 

wiiiil  it  l>.v  walking  anniinl  I  lie  tylimlir  or  tnc  kt'i|i- 
iii^  till'  I'onl  all  tlic  wliili-  taut,  liin  patli  will   Im'  that 

of  ail  iM|iial>li'  H|iiram).  ''''"'''  *'""'  '"'  ""^''""^  '^ 
ri'voliitioii  III'  will  ihircaM-  liis  distamt'  from  tlir  ryl- 
Imli-r  liyjiiHt  tlitMiiriiinfi'ifiHc  of  tlii' i  yliiiilcr.  'I'liiH 
!iiay  Ik'  illiiHtratnl.  in  a  Hiiiall  way,  l>y  usiiiK  a  miiihI 
pi'iiiil  ami  tlin  iut. 

To  const nict  till-  first  fiiriii  of  tlic  Hiiiiai  I,  ilraw 
two  xtraij^lit  lim*)*,  ii  ami  n  ", 
rnmsiiij;  catli  otlnr  at  ri),'lit- 
annlt'H.  At  till'  poi'.it  of  iiitfi- 
si'ttioii,  (haw  a  iiiall  rinlc  to 
ropi'CHciit  "'•  •  I'liil  of  a  lyliii- 

ill'y    (IV    V  •  cil'clc     irt 

callfil  till-    ..,  ;    Hiiiral. 

Let   tilt'   Mpira'  "i    tin- 

horizontal  liiu'  ..  i<"*'*   tin- 

I  I,  vertical  iiiii'  almvr  at  1.  tin- 
,  hoiizoiital  line  (lift)  at  'J.  tin-  vn-tical  liiii'  Inflow  at 
I  :\,  the  Iioiizoiital  lim'  (ri^ht)  at  1.  Tlu'  tipin's  1. 1'. 
I  i{,  t.  imliiatc  that  the  distam'.'  of  tlic  spire  from  tin- 
I  eye  of  thi' spiral  at  those  jioiiits  is,  rfspcctivcly.  (Mpial 
I  to  oiK-foiirlh.  two-fourths,  thrt'o-foiirtlis.  ami  the 
1     wlioh'.  of  the  <in'uiiift-'ri'iH f  tlic  ciiflc.  accordiiii,'  to 


i>vi>luli<iii ;  it 
Hill  li  (in'i'k 
.Ml  iIioiinuihI 
I.H  iluirartiT- 

triiiik  of  II 
1(1.  iiiiil.  it  II 
I'linl,  mill  nil- 
ir  tnc,  Kt'i|i- 
\vill   Ih'  tliitt 

III!      llllllU'S     11 

•olll  till'  cvl- 
liiiilt'i'.  'riiiM 
niii^  II  riiiiiiil 

ipiiul  I,  tiruw 

4,  II  and  /(  ", 

iiT  at   rijiiit- 

i)i:it  (if  iiitcr- 

iiall  circle  tt» 

1  of  a  cyliii- 

circli'   i.i 

,'    Httiral. 

"I   till- 

rods  till' 

^■i-  at    1.  llif 

line   Im'Iciw  at 

•  tijjnns  1. '_', 

|)irc  IVoiii  tilt' 

ctivclv.  c(|iial 

lis,     ami    till' 

.  acconliiii.;  t<» 


PN.icrivAL  itf:>nas. 


I 'J? 


till'  part  <>\'  tlic  icviiiiitioii  a 'ciiiii|iliiilicil.  I'lic  iIim- 
tuni'M  f'rnm  t>  to  4  in  tliiTt'lori'.  I'ltual  to  tin-  cirniiii* 
rcroiicc  .»t'  till*  «;ircli',  nr  woiiM  Ih>  in  an  actual 
illiiHtratiiiii  witli  a  cviiinlcr  ami  curil, 

IScliirc  lic^iiiiiiiig  til  iliaw  llic  Kpiial  itni'lt',  mark  uii 
tlic  Imrixoiital  uii!  vertical  line*  the  |HiintH  tliinii^'li 
wliicli  the  spiral  Ik  to  pass.  Willi  tlicHe  puJntK  lixcil. 
the  ciiive  can  lie  ipiite  rcailily  drawii.  Wlien  the 
Hpiral  is  liniMlicil,  the  circle  may  he  eraneil,  as  that 
loriiiH  no  part  nf  it.  hraw  a  spiral  witliniit  the  aid 
of  a  circle.  Alter  tin*  points  have  hcen  marked  as 
dii'iM  ted,  on  the  Imri/.oiit.d  and  virtiial  lims.  other 
horizontal  and  vertical  lines,  similur  to  those  in  ,1, 
may  he  drawn  through  the  points  in  assist  in  tliecoii« 
striiction  ot'  the  spiral,  it'  it  is  a  larj^e  nne.  The  spiral 
should  he  IVci|iient!y  drawn  tor  practice. 

Ill  tlio  Hi'i-oiul  vari"ty,  or  variahle  spiral  seen  ?it  <F, 

ilie  distance  hetweell  liie  ditVerelit  spires  increases 
according  to  some  re<^nlar  proportion,  as  yon  leave  the 
centre.  Tliid  spiral  may  he  illustrated  liy  the  nn- 
vvimlin^  of  a  luinl  from  a  tnincated  cone,  instead  of  a 
cylinder,  lie<iinniii>;  at  the  smaller  end.  Tin'  person 
who  unwinds  the  cord  will  liiid,  that,  with  each  suc- 
ceeding revolution,  he  increases  more  rapiilly  his  dis- 
tance from  the  cone,  his  path  In  inj;  that  »(  the  va- 
riahle spiral  (•! ). 

To  construct  a  spiral  of  thfs  character,  draw  two 
straijL^lit  liiu's,  «  and  ,/'.  crossing  each  other  at  rij^lit- 
ant^les  ate.  Draw  twii  other  straij,'lil  lines,  >■  and  f. 
crossing  each  other  at  right-angles  at  c  also :  hut 
iiiaku  tlio  angle  o  <•  .s-  slightly  smaller  than  the  angle 
.v  I'  />.      negitining    at    any   point   on    the    line   d    to 


I'iK 


rn ^rll^:l,•s•  mam  m.. 


tli.<  li^lit  ..r  til.'  Iiii-  /.  ./,  i\n  ut  'I  ixt  .•xiiinp!.-.  'Iriiw 
till-  liii«>  >i  I;  piirullfl  Willi  tlif 
liiu*  /<  /.  I'Mm  tlu>  |H»iiit  l>, 
wlittrt*  till'  liiiK  (I  A  ti)iii'li(>H  till' 
iii>lii|Mi'  liiif  ^  <lmw  /i  «/  piiral- 

1.1  Willi  tin-  li '.      I'Voiii  tin- 

piiiiit  «/.  wli.rt'  ill''  liiH'  ''  '/ 
t.nirlii's  tlif  (>l>li<|iM'  liiH-  x.  tlruw 
a  vi'iti.'iil  lint'  ilowiiwiinU  iiiilil 
It  lull.  Iu'>«  f  111  < .  'I'll"'*  I'l'"- 
J—  ,.,.,.,1  Willi   tin-  i«trniKlit  liiu'H. 

Sliiitiii«  IV.Mii  »'.  .iniw  III.'  Kpiriil  llin-iiKli  tli.'  pnintH 
wlii'if  llii-  v.Tti.'iil  iin.l  Ih.rizoiiliil  liii<'«  iiit<rM'<t. 
KiUHi-  flin  iloltfl  f.iiir.lrn<li"'ii  liiK'x.  'I'lii*  "liinil 
iiii'jiil.  of  ...iit'O'.  !>'■  ilriiwii   ill  a  niiiiiiK'r  Hiiiiiliir   l<» 

tlu>  tllHt. 

('.Vltll-KXKIHIMK    IX. 

AIISTIIAIT    ri  ItVKH.    II.M.ANt  KM    SI'lltAI,    I'OUM. 

!);iA\v  till'  .'.'iitial  iiii.'  I  '-',  lui'l  'lividi'  it  into  l'"iii- 
fi|iiul     |milH.       Tlirniiuli      111.' 

lowiT  |)oiiit    of  ilivi!*i Iiiiw 

tho  liorizoiitiil  liiH-  .'5  I.  iiiiiluiiK 
it  I'ljiiiil  l">  iMii'-lialf  'if  t  .'.  A 
liltlo  Ih'Iow  lilt'  fi'iiti"  "f  '•"■ 
iiIt|H'r  fmirlli  of  till'  v.-i'tiial  lint', 
.Imw  .".  (■».  of  till'  .■<;iiii''  li'iiKtli  11-* 
.14.  Diviil.'.'l  \  into  four  i'i|miiI 
iiiiits,  ami  ."  <>  into  nix  i'i|<iul 
|.arls.       Next    ilriiw   tin-    lonj,' 

,111-v.'.'*.  >larliiiK  tlii-iii  from   "i  uii.l  *'.,  iiml  lininli    l»y 

a.l.liiig  tilt'  siiiiiU  «iiiv«!<. 


xtiinptf.  'Iruw 

tlli-l  witli  thf 

tlic  point  1), 

A  tOlll'llOM   till* 

uw  /<  (/  piiritl- 

II,      l''ri)iii  lli« 

tilt'   lint*  ti  <l 

iif  liiK-N, ilntw 
wiiwiinlrt  until 
I',  Tliiii*  priH 
Ktriiinlit  liiii'*. 
nil  till'  piiintM 
in'H  inttrfi'ct. 
TIiIk  cpiml 
ii>r  Miiiiilur    to 


It  A  I,    KOKM. 

Ii*  it  into  four 
riiii>in,'li  tin- 
livijiii'M.  tiriiw 
i<>  .'t  I.  inaliin}; 

ill'  ..r  I  ;.    A 

cfiitru  <it'  tln> 
ic  vfr'ictil  lint', 
<iiini'  li'nj;tli  si-* 
into  four  i-ipiiil 
into  xix  ciiuul 
Iruw  tin-  loitK 
iinil  lininli    by 


I 


/•«.«»  T/r.i/,  hKttius, 


\m 


Wlu'ii  lintuiiit;  till*  «|tirfil,  fri<pniiiiy  (urn  it  up.i.lo 
■  low II  tor  t>.Hitniinttttoii.  i'lilra*  ^uunli'il  ii^ain'^t  it, 
tli<'  t-yt)  i'ii»ily  ln'rnn»'x  iti'i'iiMtitniiMl  tn  an  iTMr  in 
II  iiirv»«  lit'  tliii  rlinraitiT,  uihI  at  liii.t  .  annot  i-viii 
ilctt'i't  it.  Ily  vicwiit)^  tlic  I'liivi'  in  all  piiMititinn,  tin- 
liability  to  i-rror  i*  lr»H(>iifi|,  .\i»  a  pri'liininiiry  Wimii, 
it  will  ill'  wi'II  to  (,'ivi'  till'  lljjiiri'  Hitli  all  tlm  minor 
lini'H  oniitti'ij.      Atti-rwaril'  ilraw  it  loniplitf. 

Tin-  spiral  ii«  a  niont  iliffliuli  nirvi'  to  ilruw  well  j 
nml,  iiH  it  Im  of  tin-  llrMt  ronM'i|iifn«'i>  in  ntlni-il  draw- 
ing, it  xlioiilil  tlnrifor-  lie  niinli  prarti^f.l.  Winn 
oni'  ran  ilraw  fin-  npiral  n-ailily  ami  wi-ll,  he  will  havii 
liiit  littlt>  triMiltli-  with  otluT  I'lirvi't. 

V,\iiiATli)NH.  —  F)ruw  the  lljjnri-  in  a  nviTHnl 
position.  Alrto  ilraw  it  twioi>  uInivi*  ti  horizontal  liiii> 
pii'<i»inK  tlirou>,'li  '.',  anil  twioc  Im-Iow  the  horixontikl 
liin*  in  a  ruveriti'il  pimition. 

3qu«ra  Boiattoi  Rapaatad. 

FoitM  n.  —  Draw  a  liorizun- 
tal  lini>;  on  tlii:'  ronMtruiit  two 
equal  HijUuri'M  at  a  xli^^lit  diH- 
tuiKM'  upart.  Aiiil  tht>ir  diugo- 
nal.s  and  diaini'tiTM.  Ni-xt 
draw  till'  Hhort  ohliipu'  lines, 
tliosp  Htarting  innw  the  einU  of 
the  ilianieturM  to  he  drawn  par- 
allel with  the  diagoimls.  Add 
the  cnrven,  a  horizontal  line 
uhove,  and  another  helow. 

FuKM  I). —  Draw  two  8»iuurL'»,  their  diagonuU  and 


i'M 


tHAVHKHM'  MASUiak 


.nrtnH'itr«.  i«*  ii>  »■'""'  "  lit-*  rib'  a  rin'l"  in  •!»•!» 
ii.|tiar<'.  Miikf  fit"  .liumi'lir  i»f  tin-  xinftlU-r  .iftl.-  w 
Irillo  iiH'ri'  tliiui  •mt"«liir.l  -.1    tin-  <liiirn«'l«M   of  tli.' 

»>itit|)li<  ^■llrvt•^  tnii.  Iiinij  «lii'  riniiiiilVr <•  <•!  tlir  iihht 

lirtUn.  A.l<l  I  III'  "tiK'r  .urvt*,  itinl  u  |uirull«l  lin«' 
nU.vK  itmt  ImI.»w.  TIu'M'  tw<»  fomi*  «r«'  for  l»lmk- 
iH.iinl  li'«..ii«;  ..r,  with  u  Nli»{li»  .liiuiu.'  in  tin-  •It'- 
ll, riptioim,  thoy  L'ttli  bu  uw'l  I'"!-  <li.  luti'Mi  l»'i*»"ii». 

niOMRTIIIl'AI.  nMION. 
Willi  two  or  tliriM'  I'xfoptioii*,  tlif  ilfptiutii.  Kivfii  in 
tliiN  .liuiil.T  ar.'  Niniiily  n.'oiii.'tri.iil  ;  tli.-y  n'|»r<'*«.|it 
iH'ltlii'r  iiiittiml  nor  iirtillriiil  olijiiti*.  Hut  mi.Ii  tlo- 
ni^iiH  often  \m'*M'*n  n  nn-ut  .Ir^ri'o  ol"  Ix-iiuty.  Tlii«  '\* 
.  (.piHially  tru.'  wImii  tin'  \\m*  urc  n.ml.iiK'il  u. . '.^.lill^{ 
I.,  prill.  ipl.H  .l.riv.Ml  from  u  «tu.ly  of  niitiiri'.  <»<<... 
Iii.'tri.ul  .li'-tiniiH  luivi-  IiimI  tho  iii.l..rH-iniiit  <.f  pH..l 
tiiHt.'  ill  nil  a«iM,     Oiu  of  tilt'  vi'ry  oIiU'hI  .•riiiuin'n*'*, 

mill  til K'  wlii.li  liiiH  Ih'oii   niimt  wiili-ly  uh.'iI,  In  tin- 

(Srt't'k  fn-t.  Tlitj  Urcokn  «Iiil  not  oriniimtf,  thi«y 
only  I'luboniti'tl,  thin  ornimu'iit.  wliicli  iippfur*  to  liiiVf 
1...HI  tHc.l,  ill  Hoiiu"  form,  l«v  .v.ry  iH-oplc,  .ivilizi-.l 
iiii.l  Hiiviigc,  ivimI  ill  fv.ry  UK.',  fvoii  tli.-  rt-mott-Ht, of 
whicli  wi?  Iiiivi'  liny  record.  To-.ltiy  no  oriiiini.nt  i* 
^..  K.-n.-riilly  .■mi.l..y.'.l :  it  i*  i'nii.l.«y<'«l  l'>r  .l.'.'oriitinK 
iir.'liit.Mtiir.',  til.'  iiro.ln<tH  of  tlu'  loom,  pottrry,  in- 
ilt'i'il,  iiliiioHt  cvi'ry  tiling. 

V«'t  no  oriiiuiu'iit  coiil.5  well  be  more  nrbltriirily 
Ke..iiietri('ul,  uh  hIkiwh  by  tbe  mimple  Kiveii  in  (liinl- 
Kxen-iMo  XVII..  Kirnt  SerieH.  It  poH«uHHeH  i\  great 
(legri-e  of  repoHc  ;  it  illuHlruteH  tb«  continuoui;  growth 


fHAUUVAl  UKfilUS, 


irrli'  in  »s»i l> 
itllcr  ••irfli"»  i» 
ifti-n   uf  iIm> 

•liuiin'ffr*  liy 

l<  n|  till'  ihlKT 

iHinillil  Itnt 
ir««   f<>r  blink* 

^1'    ill    tlu'   <l<" 

I   It'lllUIIIM. 


llicy  ri'|trfn«'»l 
Hut  KiH'li  '!«'• 
iiiity.  Tliix  in 
iiicil  III  •'■ir<liiiK 
iiittiiri*.     Upi>« 

■IlHIlt    of   pMld 

r'Ht  oriiuiiK'li*''! 
ly  iiHi'il,  in  till' 
(riniiiiitf,  tlicy 

pjlcftfH  til  lllVVl' 

I'ojiU',  livilizt'tl 
IK  r«'i»«)ti'Ht,  «)l" 
o  orimiiu'iit  in 
lor  ili'i-iirittiiiK 
III,  iHittrry,  ii»- 

lon*  nrMtriirily 
j»ivt'ii  ill  (Jiinl- 
HHUHHCH  li  gri>iit 
timiout.  growth 


•»r  iJif  vim.  I    iiitii  it  ffiii  Im'  iMiaily  niixiiflpii    for  a 
Viirit'ty  ••!  |Mir|N»irii. 

Itiit  till'  I'lMiiitrii'o  wliirli  imvi<  I'lirrii'il  Ki>oiiii<trii-iil 
ili-Ki^'ii  fi.  ilif  lii^liiNt  |iiti<ii  of  |M>rfi>t'tioii  itri>  Ihom. 
wliiTi-  till'  .Moliiiiiiiiii'ilaii  ri'tirfiott  pri'VuiU  t''iirl>i<li|)'M 
liy  tlii«  ri'ii^ioii  to  iiiaki'  ri|trt'»infiitioii.»  o|  imtitnil 
olijm'U,  ilii>  |H*oplii  uni  tliiiM  i'iMii|M'lli>i|  to  rily  ii|miii 
Ki'<)iiii>triinil  oriiiiini-iit  itloiu',  Mori'p>i|iii>  iliaiun,  in 
|>iirtii'iilur,  hIicmk  what   i'Xi|Mi><iti>    ri'«iilt.   iiiuy  Im-  nl.. 

Itkiiiitil  iroiii  lliM   iiHi>  of  .mil   lim |   ii„u..riul,  wIh-u 

till'  lih.s  itri'  ••oiiibiiitMl  nil oriliiig  to  thi>  |iriiii>i|ili>.  ..t 
iiutiiri',  mill  yi-t  wiilioiit  iiiiy  utti-initf  to  ii'|iri'Miiit. 
«'viii  r«'iiii»ld^',  iiiitiutil  toriim. 


(jrRRriiiNo  —Ari' ihi' primipli*  oi  prMciiial  lUnlKri  Itunl  in 
tiii>lvr<iiin<l  /  Wlhii  of  ilu'lr  itpiilldiiion  '  Wliut  I.  •.ulil  of 
•ymimiHiiil  iiminm'im'iit  uIhihi  u  niihi'  '  ui  <ii|>iiilii(iii* 
tliux  (  oi  Mill'  .l.'.iaM  iiH'liKliiiK  mliff'. '  How  HUH  ihi'  pilmi- 
|ili'  of  •uiiiiii-iiiiril  iirniiiiri  iniiu  nlH)ui  u  .fiiiri!  Im'  ti>i't|  in  lilark- 
iMdinl  lcM<.«>ii«f  In  (lit'UlioM  li'KMini'  How  iI<h'.  -vimhm'iH.uI 
nrrunui'iiicni  im  m\  iixl*  .lltKr  (Voin  ii>tniiu'iiiriil  iirrunuiinunl 
niMmt   It  venUvi     Wh.it   io  >iti<l   ..I    ri'iiriiiinn !    (M    iu   ww  i 

Wimi  l»  Ditiil  of  rr| '     Of  liron.lili  '     lllii.triiii'  null.     Kiciii 

wliiit  III!'  till'  prini'ipk'N  of  pniiiii'iil  ilc.iun  ilirivtil  t  Wlmi  i. 
milil  of  Mriuiiiiil  .li'nljjn*  h\  \\w  pnplU  '  Wli.it  will  !.»•  iluir 
Knneo.t  fmilf  at  llr^.t  '  Wlmi  in  miIiI  of  ilii'  KiillJiH-lir  '  Why 
ihoiiiil  iIh'  xpirul  !«•  frt..|ii.iiilv  .|ii;\vn  >  WIml  U  ,iiii|  of  KioliU't- 
rKul  uriittniint  (    ;  M  iIk-  MuiiumiiKiluii  ivIlKJon  ( 


iii 


CHAPTEU    VIT. 

PRACTICAL  DESIGN. 

LEAVK9,    HUDS,    FI.OWKKS,    rONVRNTIONAMZEP. 

With  two  or  tlivcc  minor  cxcoptioiis,  all  of  the  pro- 
c.MliiiK  ..x.>rei8i>8,  wl.id.  have  illu>*tnite.l  principles  of 
,l...sigi.  in  any  way,  have  consistcil  of  g.'onu'trical  pat- 
terns, or  outUn."  representations  of  artificial  ol.jects. 
We  now  conio  to  exercises  which  not  only  illustrate 
the  principles  of  <lesign  derived  from  nature,  but  give 
eonventionali/AMl  representations   of   natural    objects. 

liy  such   representati it   is  n.eiint    that   only   the 

general  form  is  imitate.l,  —  that  the  object  is  sym- 
metrical! v  drawn  ;  all  the  minor  irregularities  being 
omitted. '  It  is  taking  the  symmetrical  before  the  un- 
iiymmrtrical,  the  conventional  before  the  natural  ;^  an.l 
this  acc..r<ls  with  sound  principles  of  teaching.  Then, 
too.  practi.uirde.sig!i  concerns  itself  mainly  with  con- 
ventional forms:  it  sel.lom  attempts  (when  it  does  it 
violates  the  best  taste)  an  exact  representation  of  na- 
ture. Even  the  highest  art,  as  illustrated  in  .statuary 
and  painting,  though  foumled  on  the  imitation  of  na- 
ture, .r<.es  farther  than  mere  imitation,  and  gives  a 
renderip"  of  nature  in  harmony  with  the  requirements 
of  the  most  cultivated  taste.  It  is  only  in  the  paint- 
ing of  flower.s,  fruits,  and  the  like,  that  an  exact  imi- 
tation of  nature  can  be  properly  attempted. 


Hi 


I'UACnCAL  UKSUiN. 


^m 


ONAMZEP. 

[ill  of  the  jire- 
jirinciplort  of 
)iiH'trical  put- 
iticial  olijccts. 
Diily  illiistriito 
itiiif,  but  give 
.tuiiil    objects, 
bat   only   tlii^ 
(bjcct  is  syin- 
ilaritk's  bciiij; 
before  tlie  iin- 
•  natural ;  ami 
filing.     Tben, 
,inly  witli  con- 
ben  it  does  it 
Mitation  of  na- 
ted  in  statuary 
nitation  of  na- 
1,  and  gives  a 
le  requirements 
y  in  tbe  paint- 
t  an  exact  inii- 
pted. 


Tile  following  exercis..s,   A,   I!,  C,   I>.  K,   illustrate 
tbe  power  of  repetition  in  nnndiers  on  form: 

CODventionol  Leaves  Bymmetrioally  arran«ed  about  the 
Centra  of  ao  Equilateral  Triangle.    The  Power  of  3. 

Draw  an    e.piilateral   triangle.     Divide   oacb   side 

into    balves;    and,  from  eacb 

point  of  division,  draw  si  line 

to  tbe  opposite  angle.     Tbis 

will  divide  tbe  triangle  into 

six  equal  i)art8.    In  eaib  tbird, 

draw  a  conventional   leaf,  as 

seen    in   tbe  copy  (A).     Add 

tbe  curves  near  tbe  centre. 
Observe  tbat  in  making  eacb 

of  tbeso  live  designs,  A,  I>,  V,  a. 

1),  K,  we  bave  used  tbe  same  elements;  modifying  tlnin 

just  enougb  to  adapt  tbem  to  tbe  spaces  to  be  filled. 
Tbe  leaf-form  \vbi<;b  lias  been  used  is,  of  course,  U 
bigldy  ccmventional  one. 

Require  your  pupils  to  make  new  designs,  by  com- 
bining, in  a  similiar  manner,  tbe  leaves  and  otber 
forma  given  on  tbe  cards.  Tbis  is  one  of  tbe  Hrst 
steps  in  design,  putting  old  forms  into  new  combina- 
tions, and  will  bo  found  exceedingly  pleasant  and 
profitable  for  tbe  pupils. 

Wben  a  pupil  bas  made  a  new  design  on  bis  slate, 
permit  bim  to  reproduce  it  on  tbe  blackboard  tbat  tbe 
wbolo  scbool  may  see  it.  Tben  require  bim  to  tell 
bow  ho  drew  bis  design,  and  describe  tbe  principles 
wbicb  it  illustrates.  For  tbe  pupils  to  de.scril)e,  in  a 
like  manner,  any  of  tbe  card-exercises  will  be  very 
serviceable  in  giving  tbem  a  command  of  language. 


134 


TKACUKHH '  MA y UA L. 


Conventional   liOaves  •ymmetrtoally  arranged   about  the 
Centre  of  a  Square.    The  Power  of  4. 

Dniw  !i  s'luari",  its  »liiiint;ter.s  und  dingnnal:*.  Add 
t*triiight  liiii's  coiiiu'rting  the 
••lids  ol'  tlu'  diimu'tiTH,  and 
divide  tliciu  into  thirds.  In 
ciich  t|iiiirtfr  of  tlio  wtjimrp, 
di'uw  ii  I'onvi-ntiunul  leaf,  an 
M'cn  iit  I{.  Add  the  curves 
ni'iir  the  centre,  the  outer 
points  of  the  triiiiiguhir  forms 
fulling  on  the  centres  of  the 
semi-diiiineters.  <iiv('  this  as 
ii  IthicUboiird  lesson,  following  the  method  described  in 
the  last  chapter. 


Conventional  Zieaves  aymmetrically  arraniced  about  the 
Centre  of  a  Pentagon.   The  Power  of  5. 

Draw  u  circle  on  its  ii.iri- 
zoiital  and  vertical  <liaiiieters. 
Krase  the  hori/ontal  diameter, 
and  divide  each  half  of  the 
circle  into  five  e{|ual  ]iarts, 
making  ten  ei|iial  parts  in  ail. 
Draw  straight  lines  uniting; 
the  alternate  pujnt.s  ,,\'  divis- 
ion :  these  chords  will  fnini 
the  sides  of  tin;  peiitagun.     In 

each  fifth  of  the  pentagon,  draw  a  conventional   leaf. 

us  seen  in  the  copy  (C").     Add  the  curves  near  the 

centre. 


«■! 


A- 


iged   about  the 
of  4. 

[igonals.     AiM 


d  dfijcribed  in 


liced  aboui;  the 
rof  6. 

■  on  its  Ihii'i- 
••al  diatiH'tiTs. 
iital  dianictiM-. 
1  half  of  till- 
<'()ual  jiarts. 
al  ]iarts  in  all. 
lini's  uniting: 
lint.s  of  ilixis- 
nls  will  form 
|ii>nt!i^oii.  In 
'<Mitiona1  li'af. 
rv.'s  iioar  flic 


I'HACriVAL  DESIGN. 


VMi 


Conventional  liCaves  iymmetrloaUy  arranKed  about  the 
Centre  of  a  Hexagon.  The  Power  of  6. 
Draw  a  circle,  and  divide  it  into  twelve  <'«|iial  j  artw, 
or  sectors,  by  first  dividing  it 
into  halves,  then  into  fourths, 
and  then  each  fourth  into 
thirds.  Draw  chords  connect- 
iiig  every  other  point  of  di- 
vision :  these  six  chords  will 
form  tl!e  .sides  of  the  hexajjon. 
In  eacli  sixth  of  the  hexapin, 
draw  a  conventional  leaf,  iis 
seen  in  the  copy  (D).  Aild 
the  curves  near  the  centre  of  the  hexagon.  The 
outer  points  of  the  curved  triangles  terminate  at  the 
centres  of  the  semi-diameters  of  the  hexagon. 

Conventional  Iieaves  symmetrioally  arran«ed  about  the 
Centre  of  a  Oirole.    The  Power  of  8, 

Draw  a  circle  of  any  given  diameter,  and  divide  it 
into  sixteen  equal  part.s,  or  sec- 
tors, first  hy  dividing  it!  into 
halves,  then  into  fourths,*  then 
into  eighths,  then  into  six- 
teenths. Draw  a  .second  cir- 
cle, having  the  same  centre 
and  one-fourth  of  the  diameter 
of  the  lir.st.  In  each  eighth 
of  the  large  circle,  draw  a  con- 
ventional leaf,  as  seen  in  the  U. 
copy  (E).  Add  the  curved  triangles  near  the  centre. 
The  ba.ses  of  these  triangles  are  parts  of  a  circle  hav- 
ing a  diameter  etjual  to  one-third  of  the  diameter  of 
the  large  circle  Analyze  this  design,  and  sec  how 
simple  are  its  elements. 


i:t<> 


TE.WIIKUS'    .MAMAL. 


V'ou  will  Kooii  lind  tliiit  the  imitils  wlio  draw  bcHt 
(III  not  iilwiiys  succiu<(l  licst  in  original  designs. 
Miinuiil  skill  and  inventive  {lower  are  not  always 
united  in  e(|ual  proportions ;  lienet^  it  will  soinetimes 
happen  that  a  pnpil,  discouraged  by  his  poor  inaininl 
»'xeeution,  wi'l  takct  heart  again  when  he  begins  origi- 
nal design,  becausti  he  succeeds  so  well. 

OblonR  RoMtt«  of  Irregular  Oonventional  liOavea. 
Draw  un  oblong,  making  its  width  two-thirds  of 
its  lengtli.  This  can  be  done 
by  drawing  the  vertical  line  5 
(),  dividing  it  into  thirds,  and 
then  drawing  1  T)  and  r»  2, 
each  ecjual  to  one  of  tlie  thirds. 
In  the  same  manner,  draw  .'5  4. 
Then  add  1  .'I,  2  4,  and  draw 
7  H  through  the  centre.  On 
the  diameters,  draw  four  ogee 
curve.s,  drawing  each  curve  from 
one  end  of  the  diameter  to  the  other  without  stopping. 
Next  draw  the  slightly  curved  lines  which  form  the 
midribs  of  the  leaves,  and  then  the  (Mirves  forming 
the  lobe.s.  Now  draw  the  two  short  curves  which 
meet  on  eiwdi  semi-diameter  at  a  distance  from  the 
centre  of  the  oblong  ecpial  to  one-half  of  a  short 
semi-diameter.  Where  these  curves  meet,  add  the 
lierries  as  seen  in  the  cop}',  two  on  ciich  sliort  senii- 
dianietcr,  and  three  on  e.ach  long  semi-diameter. 

Variation.  —  Draw  a  .scpiure  rosette  as  in  the  pre- 
ceding exercise;  then  add  the  berries,  two  on  eacii 
semi-diameter. 


VHAVTWAl.  hKSKjy. 


1»7 


ili<»  (Iniw  bi'st 
iiiial  (Icsigim. 
o  not  always 
'ill  H()iii(;tiinea 
[Kior  maiiual 
•  l)t'giiis  origi- 


lal  liOavea. 

two-ill ir« Is  of 
(1111  bc^  (lone 
•crtical  litit;  5 
:o  tliinlt),  mid 
I  ')  ami  r.  2, 
of  tlic  tliirdn. 
ficr,  draw  .'{  4. 
4,  and  draw 
coiitro.  On 
aw  lour  ogee 
leli  curve  from 
lout  stopping, 
licli  form  tlic 
irves  fonning 
eurvcs  wliich 
net'  from  the 
If  of  a  short 
nect,  add  tlie 
li  sliort  seiiii- 
liametcr. 

as  in  the  pre- 
two  on  each 


Square  Rosette  of  Irrejiular  Conventional  Leavei 
Draw  a  wquan'  and  its  diaimtcrs.  and  on  the  latter 
draw   four  ogi'e   curves.      Next 
(haw  the   four  slightly  curved 
lines   which  form  the  midribs 
of    the   leaves ;    then   add   the 
curves  forming  the  lobes.     Ob- 
serve  that   while  each   leaf   is 
slightly  irregular,  the  four  are 
just    alike    and    aymm"tiicully 
arranged  about  the   centre   of 
the  S(juare. 

IjOtuB-Flower  Boiette,  Square. 

Draw  a  s.iuare,  its  diagonals  and  diameters.  Par- 
allel with  the  diagonals,  draw 
tlie  lines  which  form  the  out- 
lines of  the  lily  or  lotus-flow- 
ers. Draw  the  central  leaf 
of  each,  and  finish  according  to 
the  copy.  This  can  be  easily 
used  for  a  blackboard  lesson. 

The  lotus-tlower  is  an  Egyp- 
tian ornament,  symbolic  of  the 
Nile,  source  of  fruitfulness  and 
plenty. 

Vauiation.  —  Instead  of  drawing  tlie  lotus  flow- 
ers oil  the  semi-diameters,  draw  them  on  the  semi- 
diagonals,  lie  certain  to  retain  the  general  charac- 
t(!riatic  of  the  flower. 


i:tH 


rh:.t(IIKUs'   M.tMAL 


Lotui-Flower  Rosette,  Obloug. 

Draw  tlio  lino  1  2,  and  (liv'dc  it  into  tlirco  <>i|uul 
piirts.  Miiko  till'  i>i)(!s  (if  till' 
oliliiiig  vi|Uiil  to  two-tliiriiti  lit' 
1  '2.  (.Vitn|'!eto  the  oblong, 
anil  draw  itH  diagonalH  and 
short  dianu'trr.  Conni'ct  tlic 
rnds  nt"  tilt!  diaini'ters  liy 
straight  lineM,  and  divide  thorn* 
into  fiiurthH.  Parallel  with 
till'  diai'iinals,  ilraw  the  linos 
tbrniiii>;  tin-  outliiii's  of  tho 
lotus-tlowors.  Adapt  each  flowor  to  tho  space  to  ho 
lilli'd.  This  illustrates  Hymmetrical  arrangement 
around  the  centre  of  an  ohiong,  and  will  «ervo  for  a 
hlikklioard  lesaoii  by  the  teacher. 


Blackboard  and  Charts. 

See  that  3'iiu  iiiaki-  only  a  proper  uao  of  the  black- 
liiianl.  If  yiiu  attempt  to  teacli  a  class  wholly  from 
that,  making  your  hiaiklioanl  copies  take  tho  place 
of  all  printed  copies,  then  it  is  absolutely  essen- 
tial that  you  he  abh-  to  draw  both  rapidly  and  beauti- 
fully. The  development  of  taste  is  one  of  the  chief 
objects  of  drawing:  that  cannot  be  secured  unless  the 
pupils  have  beautiful  copies,  models,  to  look  upon  and 
to  draw,  —  the  more  beautiful  the  better.  Scarc'ly 
any  one  can  draw  with  suflicient  rapidity  and  beauty 
to  pr.iviile  such  c()]iies  wholly  from  the  blackboard. 

Hut  this  is  not  all.  When  pupils  draw  from  luipies 
on  the  black iioard,  if  the  class  is  large,  only  a  few  of 


to  thn>o  ei|uul 

('    I'lu'.X    (if     tilt' 

two-til iriiy  (if 
I  tlu>  nbluii^, 
Lliu^oiinlH    lUid 

Connect  tlic 
(liainctiTH  hy 
1(1  divide  tlu'sc 
I'ariilUI  with 
tt'iiw  tlio  lincH 
itlincM  of  tlu^ 
IV  Hpnco  to  bo 

Hrriuigt>Mit>nt 
rill  Hurve  for  ii 


of  the  bla(!k- 
Hs  wholly  from 
tivko  the  place 
lolutely  e.sxcn- 
lly  and  beiinti- 
e  of  the  chief 
ired  unless  the 
look  upon  and 
:ter.  S(!arc>ly 
ty  and  beauty 
blackboard. 
aw  from  cuipies 
,  only  a  few  of 


I'llACTICAI.   //A.'.S/'/.V. 


l:J!» 


the  whole  numlier  can  obtain  a  ^"""l  *''''*^'  "^  •'"' 
copy,  —  tlie  few  wild  sit  directly  iu  front.  For  those 
who  nit  to  the  right  or  to  the  left,  every  line,  except 
vertical  ones,  is  foresh(irtene(l ;  that  is.  the  fore  <>v 
front  view  does  not  give  the  true  h-ngth  of  the  line, 
bei;aiise  it  is  seen  iibli(pu'ly.  Thus,  a  sipnire  appearn 
to  bo  an  oblong;  a  circle,  an  ellipse;  all  but  vertical 
lines  are  distorted;  forms  which  may  lie,  in  reality, 
beautiful,  lose  all  their  beauty.  While,  therefore, 
only  a  few  of  those  having  good  vision  can  »oe  the 
blackboard  copy  as  it  is,  others  having  defective  vi.s- 
ion  cannot  see  it  at  all  becau.so  of  the  distance. 
These  sauio  grave  objections  hold  against  drawing 
from  churta,  and  so  they  are  forbidden  to  be  used  iu 
the  best  European  schools. 

Hence  it  is  absolutely  essential,  if  pupils  are  to 
make  satisfactory  progress  in  drawing,  that  each  one 
should  have  beautiful  copies  placed  in  his  hands ; 
and,  in  addition  to  these,  there  must  be  beautiful 
models,  and  alw.iys  rle<ni,  whatever  their  coldr,  when 

he   conu'S  to  draw    from    the    solid.     'rins pies, 

in  the  hands  of  the  pupils,  greatly  diminish  the  labor 
of  the  teacher,  and  are  absolutely  essential  for  devel- 
oping the  taste  of  the  pupils. 

As  fre(piently  affnined  before  this,  the  blackboard 
has  its  important  uses.  For  illustrating  principles  it 
should  be  oft(Mi  employed,  since  you  can  then  instruct 
a  whole  class  jvt  onoo.  Uu(le  drawings,  rapidly  exe- 
cuted, are  usually  sufficient  for  this  pur[iose.  Then 
it  is  essential  that  you  should  often  draw  on  the 
blackboard  the  tigure  which  the  pupils  are  drawing 
from  their  copies  :  you  can  thus  keep  the  whole  class 


t«> 


r^:.iriii-:uy  mash.h,. 


tit^cHuT.  tf'uili  itll  lit  oiiw  liow  to  draw  tin-  nivcii  tiff- 
lilt',  Mpiir  till'  iiiil<i|i'iit  t<»  uniitJT  activity,  iiimI  rcHtniiii 
tilt-  ovcrliiiMty.  Ajiiiiii,  it  in  Honu'tiincH  well  to  j^ivc  on 
tlii>  liliitlilioiinl  t'litiit'ly  new  i'X<'r<  ifti-w,  tliui*  <'oni|U'll- 
iiij;  the  iMipilM  to  oImitvi'  ciirt'l'iilly  every  Htcp  you 
liikc,  mill  to  rcpi'iit  tin-  HiiiiiK  litter  you.  Also,  lor  tlie 
purpoHe  of  verifying  tlietiition  exurciHOH,  you  tnuHt  use 
the  liliu'klxniril;  otlierwisu  you  must  tul«e  time  to 
exiimiiio  the  work  of  euch  pupil  'V[iiirutely,  however 
lurj;«!  the  cIiihh  miiy  he.  Thin  limited  umu  of  tlio 
hlaekhoiinl,  iiiid  thin  only,  hiin  the  iipproviil  of  the 
lie«t  experience. 

Kemeiiiher  that  several  thiiiHH,  in  the  way  of  din- 
eipliue,  are  to  be  aimed  at,  and  the  moile  of  instruc- 
tion miint  l)fl  mnditied  accordingly. 


(!AKn-KxEKCISK   X. 

OonventionallBad  Lekf, 

Drawtho  vertical  lino  1  2,  and  divide  it  into  thirds. 
Make  il  4  ('([ual  to  two-thirdn  of 
1  '2.  Draw  the  dotted  curves 
forming  the  boundary-line,  and 
then  the  other  horizondtl  linos. 
Next  draw  the  curves  from  the 
endu  of  the  liori/oiital  lines  to 
the  verticaliine.  Finish.  This 
is  the  conventionalized  form  of 
no  parti(;ular  leaf.  Observe  that 
it  is  built  oil  tho  abstriv<;t  curves 
in  Card-exercise  XXVII.,  of  tho  First  Series.  This 
illiiHtrato.s  Hymmutriial  arranRoment  on  an  axis. 


r 


PHACIHAI.  UK'^liiS 


Itl 


till-  j,'iv('ii  Wff- 
y,  mill  n'Mtniiii 
wi-ll  to  n\v»'  on 

tlllH    riinipfll- 

very   Htcji  you 

Alrto,  for  till' 

,  you  tniut  UHi> 

tiiko  tiiiu*  to 
•utcly,  liowcvfr 

h1    Ui*0    of    1 1  If 

pprovttl  of  tliL' 

lie  way  of  (liM- 
imIc  of  inntrui'- 


I'  it  into  tliinls. 
:o  two-tliirils  of 

dottf'il  furvcM 
ixliiry-liiio,  iiiul 
orizontal  liiius, 
virvi'S  from  tin' 
i/oiit;il  liui'.s  to 

Finish.  Tliis 
lali/.t'd  form  of 
f.  Observe  that 
ubstriuit  curves 
t  Series.  This 
I  ail  axis. 


Caki)-I''xku»m»k  XI,  I 

Ofooui  riow«r,  Oon**ntlon»Jl««d 
Draw  th.«  vrti-al  line  I  L'.  ami  .livi.l<<  it  into  He^•en  , 
«M|ual  parts.  Draw  .»  l  ainl  '» 
(i  e(|iuil  to  four  of  I  he^e  |u»rtH. 
Join  tliM  entU  of  thiwi  horizon- 
tal lines  l»y  vortical  lines,  uinl 
draw  7  H  throu^'i  the  sec- 
iMid  point  of  division  from  the 

top.     Draw  the  lonK  <'urvcH  of 

the   tlower  llrst,   and   then    the 

shorter  ones.       Here   we    have 

another    illnatratioii    of    sym- 

nietrical  arran^jiiujent  on  an  axis. 


Cakd-Exkkcisr  XIL 
OoDTolvulus  Bud,  OonTontlori»lt«ed. 
Divide  the  vertical  line  I  2  into  thirds.     Make  .1   I 
equal    to    one -third    of     1     2. 
Sketch     lightly     an    unbroken 
boundary-line     of     tho     whole 
bud;  and  then  finish  as  in  tho 
copy.     Obser>-e  that  one  of  the 
curves  passes  through  the  up- 
per  point   of    division   on    the 
vertical    line.       Froni    the    ne- 
cessity of  the  case,  tho  drawing 
of  the  spiral  portion  of  the  bud 
cannot  bo  perfectly  symmetrical  above  the  cup. 


IKAVUhmt'  MAMAL 


<.'AKI».KxK.lt(  IHK  XIII. 
■prtxorOonvolvului,  Convantlonaliiad. 
f>rnw  fv  viTfi.vil  lino  (,f  „|,y  ^Jv,.,,  |,.|,j{t)i,  ahtt 
Imlvf  it.  Muk,.  1  'J  „,j,,«|  to 
tlinc-lourtl'  or  tilt'  v.Tliciil 
liiif,  mill  .1  I  vi^  at)  fii  tliri'c- 
foiirtliH  of  I  'J,  Uruw  tilt" 
^»iHi  tunc*  Iroiu  till'  i<rii|  of 
.'I  4  to  tlip  cpfitrw  eif  I  2,  or 
\t<ry  ii.ui-  it.  On  tK«»  lowtr 
thinl  of  tlm  iiii|iir  Imlf  of  tlit* 
v.Tticul  tini',  draw  llii-  nil^x  or 
I'lip  of  thf  Mower;  unil,  on   tl)t> 

u|i|M'r  thinl,  liniw  tlni  o|mii  oomllti.     Front  flic  i-fntrt' 

<«f   1    -',  tlruw   live   l('uvi"«,    !ilw»  two   iiiiopciifil   !iimIm. 

Si'«  thiit  till"  |Mi{iiU  iiinko  their  Uruwiuyd  mucli  l(ir((«'r 

tliiui  tho  ropy. 

C'aki)-Kxki«;.mk  XIV. 
l)"»l»n  fVom  the  Oonvot* uiu*  Flowtr. 

l)raw  11  ^<^n^l'•l'.  itn  (liiiini'tcrH 
iiinl  difigoiiuls.  In  tin-  npfu'r 
qiiurti'r  of  till!  h<jimr«',  on  rlio 
Humi-iliunH'fi'r,  ilruw  ii  lonvol- 
\uln«  tloMiT,  n>*  yivcn  in  tin- 
'•<'j>y, — 'Wliicli  \*  tliu  Bjinii'  lis 
the  flowi'r  in  the  lu-t  ox<'n'i>n', 
—  uiul  I'pi'at  ill  I'iicb  of  tlif 
otlicr  tlircc  quarter?*.  Make  tin- 
lifit;lit  of  till'  taivx  at  tin-  liam* 
of  till!  Huwi'r  ttliout  ont'-fourtli  of  tin-  Ki'mi-iiiunifti'r. 


I'HAtflVAL  itKfluX. 


149 


I    It'iiKth,    aiwl 

t   'J  I'H'.in]   til 

tlifl    viTlital 

',  JttI   U>  tliri'o- 

I'niw     fill' 

It  till'    I'liil  iif 

r«  iif   1   1',  or 

l>tl     tllC     liiWiT 

iir  half  of  till' 
I'  till'  ii\\y%  or 
;  aiitl,  oil  il)i> 
oin  fin iitri* 

l(>|M'llCll     iltlllx. 

It  iiiucli  ltirj{t'r 


iw«r. 

itH  iliatnoroni 
[ii  llui  iiiiiH'r 
|iiiir<',  on  till) 
iw  Ii  ri>iivoi« 
given  ill  tlii> 
till!  H!inu>  nx 
la-t  t'xi'nini', 
eui'b  of  tlio 
it.     Miiki'  till' 

X  III    tllu    liJlHU 

L-uu-Uiunicti.<r. 


h  liiiK  !«'fii  tail!  Iliiit  iIm-  lift  i.fi'|>  iu  tlf.i«ii  I*  t»» 
•nki'  II  f'ttin  iilri'Utly  tlrnwii.uriil  mi  iinf  it  m  t.i.|iinHiiii« 
,t  iii'W  <;iinil>in!»tioii.  I'ii|iilit  of  nil  UK'>«  l"Vi'  tu  ilo 
ttiiit,  wliifli  iit  uii  I'Xfriiftt'  piirti}'  iii  ilrii«iiiu  iiinl 
imrtly  in  iiivi'iitin^. 

l)o  iM)f  forxi't  to  roqiiiro  tlio  |tn|iii»,  fMiii  tiiiii'  to 
tiini',  to  iiiialyzti  ilin  tiir<l  fXfr«i«ii4  km  f\|iluiiif<l  in 
•liB|itt'r«  two  iinti  tlin-,  Ix't'on*  lH«iiiiiiiig  to  tlriiw 
llioni.  'I'lify  iiiii:.t  now  tlcwrili'i  iio».  only  tin'  liin'< 
lilted,  but  llu'  MrintipUH  of  tli'r.ij^ii  illuKtrut«M|. 

CA»l>-Kxi-.KrlrtR  XV. 
Symmetr'CM  Moroiqua  Ornkmeni. 

I>ruw  II  viTticiil  lini>  of  any  uivt-n  Ifiitfth.  iiiwl  <Ii- 
vi'le  it  into  four  i'«|iial  |MirtM. 
Miikt!  1  '_',  .'I  4,  r»  Ci,  tM|Uiil  to 
Ilirt't'-foiirtliH  of  tlic  viTliiiil 
lino,  iukI  7  H  tM|mil  to  oiic- 
lialf.  Di/idf  t  '2  into  tliinit, 
giving  tin.'  iiroportion*  of  tin- 
trefoil.  First  draw  tlio  lon^ 
tiirvoH  from  t  2;  then  tlif 
(iirvca  from  M  4.  Finish  liy 
(Irawing  tint  itliiirt,  tiiiii|>l(' 
tiirvci.     Muku  ul!  tliu  eurvtH  as  gro^-eful  m  poasubk'. 

Vakiation,  —  HiiYiii){  drawn  tlii«  fij»Mr('  iih  given, 
ri'iieat  it  on  tliu  lower  side  of  •">  <!,  drawing  it  liottniii 
ii|'.wurdii.  It  tlien  beeomcH  »  iiiaper  iiutteni,  and 
iiiuy  Ih!  encluiied  in  u  reituugle. 


m 


TfiArilKH"'   .MAWAI^ 


<'»»!)>  Kxmti  inr,  XVT. 
Mur««<iu«  OrnamtBi  •rranM't  m  •  OroM. 
Itruw  A  •••|iiitn*.     At   tlii>  I'fiitri'  of  imm'Ii  ohli*  <>f 
ilio  »)|tiitri',   ilrikw   Ik   liiit>   |M'r- 
;>i<iiilii'iilar   to    tliK    Hi<|i>,    ami 
'>iii>-tliir<l     li>ii({i>r.      •)n     tlii< 
liiii>,    uml     tliK    Niilo    of     ilii> 
«|iiiir<s  <lrim  tin*    form    Kiv>'i* 
III     tliti      liiitt      cunl-fxirii^t'. 
liiMiili'     I  III'    Ni|utiri-,    ilruw    Ik 
nmt'tto,   lik"    'I     ill    <'urili'X<'r- 
I  ii4o    I.     'riiiM   illuHtriUiM   li<>«v 
I'ikMy  n  tliiii}{  it  it  to  coiiiliiiu* 
Kiv«>ii  utiitN  mill  iiiuku  now  <lfitiKiii«. 

<!AHIt-KXK.H<'IHK  XVM. 
Vertloal  B*p«tltlon.  -  laUrlMltn  •oil  Trefoil  Formt. 
|.*oiiM  a.  —  Dniw  tliti  vcrtiful  lint'  1  'J,  mi'l  "I"'"  it 
conntritit  tlirt'o  Hqiiuii'!*,  tinifliiii); 
nio  iiimtliiT.  Priiw  ill"  liori- 
/.oiitul  (liuinutnrM  <>f  thi>  Mi|iitir)'i*. 
Diviti**  tlicHC  iliuiiH'ti'rH  un<l  I  Ik* 
liori/oiitiil  HJilfi  iif  tlif  Ki|imii'n 
iiitii  luiir  tM|iml  jmrtH.  Miiiw 
till'  olilii|tii<  lilivM  wliii-li  iiiti'i- 
iiii'i)  iiv  tJi'iiifj  oviT  mill  umli-r 
.•mil  otliiT  ulti'i-iuiti'ly. 
I'liicM  /'.  —  Dniw  tliri'it  mjimn-H 
UN  ill  till'  liiHl.  Ill  ••iiili.  ilriiw  II  tn-foil  lenf,  not  iiP  >w- 
iii^  its  IoIk'h  «.»  tmirli  i-itlicr  xiilf  »(  tlic  H«|iiiir«'.  Kmli 
of  the  Htiiull  liiili'M  tukurt  up  oiii-Mixtli,  uml  ••adi  of  tlm 
Hiiiiill  iliuiiioml  Hliuiit'H  two-»ixtli»i,  of  u  biJu  of  a,  mjuure. 


.  ,•:.. I    lv^-o*,J 


r 


^HJVnVAL  I/Aa/U.V. 


iiri 


•  CroMk 

IW  II  liiiti  ptT- 
till'  fu\o,  itml 
[ur.  <  >n  tliU 
niiU*  of  tli)> 
h<*   fonn   ant'U 

|U»rf,    ilriiw    It 

ill    fiinl'i'Xi'r- 

illuHtriitiM    liow 

it  in  to  ciiiiil>iiii< 


rrafolll  Fornn. 
I  'J,  mill  ii|Miti  it 
i|uui'i''<,  loiicliiii^ 
Pmw  ill"  liori- 
I  of  till'  Mt|iiuri'i«. 
iint'tcrH  iktiil  till' 

iif  till'    r«|llurcM 

1    piirtM.      Diiiw 

vn  wliii'li   iiifir- 

ovcr  mill    iiiiiliT 

iiiiti'ly. 

iiw  tliriM*  wjimriM 

I   ll>ut',  not   lll'')\V- 

('  8i|iuin'.  I'imli 
,  tiiiil  «'iu:h  of  tilt) 
»i  Ju  of  »  tttiuure. 


CJanm-Kxkni  iMK  XVtfl. 

■oftunnUl  N*9«lllion.  -Trafbil  r>>rmii,  »ii(t  InUrUalng. 
|<'iii(M  II.  —  |)rn\v  liiiir  -i|iiiui ••  iiiiitiil  lioii/iiiiiiilly, 
uml  itild  llii'ir  vi't'tiiiil  iliiiiiK- 
(■•r*.  I itt^lifM'  iliitiiii'tirit. ilmw 
Iri'fiMl  lt'(»vin,  i\t  ill  till'  ••■•p.v 
Mritw  i\  liori/iiiiiitl  liiti'  uIhivi', 
iiiiotlicr  Ih'Iiiu, 

FnitM  /),  —  Draw  fitiii 
M)iiiiri'4,  iiiiiliMl  Imri/.  iiitully 
I'ill  lltfMf  M|iiitri>M  with  iiiti'r- 
I  u'iiig  jiiii'it,  M  ill  II,  liiitt  I'unl- 
i'<t'r»'i»»»,  l>ru\s'  it  Imri/H'iitiil 
lint)  iihovr  iumI  lii'liiw.  |iivii|i>  till'  ii|)|M'i-  liiiii/.oiiiiu 
liiii>  into  lmlvi'4;  on  t'lu'li  liitif  loiiNtriiit  ii  Mi|iiiiri',  uml 
nil  it  witli  It  tri'foil  Ifuf,  nn  ill  tlii>  copy,     Tn  cuiiipli'tK 

till'  lllnllliliti^,  ill'ikW  Ii  liiil'i/oiiliil  lllio  uIhiVi'. 

Hqu«r«  IloMtta  of  Uooyantlonal  L«»vm,  ancl  MouldlnR. 

I 'raw    till!    Mpiuri',    itN    iliu^iiiiulH    uml    (liiiiiiiti'rH. 
Muki'  till'  iliuiiK  tor  of  tlif  cir* 

•  It'  lit  till'  ri'llll'i'  ''i|lial  to  illll'- 
tolll'tll    of  till'    iliuilll'tlT   of    tliu 

M|Uuro.       1)i'a\v  I  lie  coinpoiiiiil 

rllI'VcM  oil  till'  iliuKullul(«.       Nl'Xt 

ilruw  till'  lt'uvi'«  nil  tlu'  iliuiiu'- 
tiTH,  uml  lliiir«li  liy  ilriiwiii^ 
till'     iiiurKiiiH     of     till'     otlit'i- 

ll'UVI'M.         Mlllil'     tiic     Miillll     of 

tlii>  iiiniililiii^  Im'Idw  till'  i-iMfttt' 

I'ipiul  tu  oiii'-tliii-tl  of  «.  '>iil('  of  till*  Hi|iiuri'. 


§ 


14U 


TKACIIKHS'   MANUAL. 


Vaimation  1.  —  Draw  til rec  sfiuiircrt  uiiiti-d  liori- 
/...iitiilly,  and  iill  tliciu  in  a  siiuilar  muuii.-r.  Cdii- 
tiniu!  tilt"  niouldin),'  l»c'low  Hio  rosottes. 

Vaimation'  2.  —  1  raw  lli"  wiuaro,  its  diagonals 
an<l  dianiftcrs,  and  tlir  lirck-  at  the  (H-ntr.-.  Then, 
iiiMteud  of  drawing  the  eompound  curves  on  the  di- 
agonals,  draw  them  on  the  diameters,  and  the  leaves 
on  the  diagonals.     Finisli. 


t'Ai{i>-KxKU<'isr.  XIX. 
Toy  Oburoh. 

Draw  a  square,  and  divide  it  into  nine  iM|u:d  small 
squares.  Erase  tlie  right 
two  of  the  upper  three.  l)i- 
vide  the  right  and  left  sides 
of  the  renmining  upper  S(iuaru 
into  thirds,  and  the  top  into 
fourths.  Through  tin-  lower 
points  of  division  on  the  sides, 
and  the  outer  points  of  divis- 
ion on  the  top,  draw  the  in- 

dining    sides    of    the    spire. 

The  window  occupies  one-half  the  width  of  the  square. 
Draw  the  vertical  and  liorizontal  lines  belonging  to 
the  spire  and  body  of  the  church;  then  add  the  lines 
for  the  roof,  door,  and  windows.  Draw  the  lower 
lines  of  the  roof  before  the  upper  lines;  observe  that 
the  ridge  is  level  with  the  bottom  of  the  spire. 


cfl  united  linri- 
inuiMKT.     ("on- 


',   its    (liiigoniils 

(H'litrf.     TluMi, 

rvi's  on    the   tli- 

UIkI    tllf    ll'llVfH 


line  (Mjuul   HiiiiiU 
raso     t)ie     right 
pper  three.     1  Ji- 
lt and  left  sides 
ling  upper  stjuare 
imd  the  top  into 
rough   tin-  lower 
isiou  on  the  sides, 
r  points  of  divis- 
top,  draw  the  in- 
s    of    the    spire. 
dth  of  the  square, 
nea  belonging  to 
hen  add  the  lines 
Draw  the   lower 
ues;  observe  that 
F  the  spire. 


l'HA  cue  A  L  UK.SIUS. 


14( 


('AUI>-K.\Klt<I,SK    X.\. 
Fuohaia  Conventionaliged. 
I)niw    1    1',   and  divide   it   into    four  equal    piirtv 
Make  ;{  I  equal   to    1   L'.     Join 
ends   of    .'{    4    to     the     upper 
end   of    1    '2   h}'  oblique    lines, 
and    draw    o    G    through    the 
eentre     of     the     lower    fourth 
of   1    '2.     Finish    the  form. 

\'.\KiATiiiN-.  —  1  )raw  a  circle, 
and  <livide  it  into  six  equal  parts 
by  drawing  three  <liaineter.H.    On 

every  other   senii-dianieter,  draw  a   form    similar  to 
this,  with  the  stems  of  the  three  uniting  at  the  centre. 

C.VKD-KXKUCISK    XXI. 
Fitober,  lUustratinic  Compound  Curves. 
J)ivide    tile    central   vertical    line    into    four  equ.nl 
parts,  and  make  1  2,  3  4,  equal 
to  two  of  these  parts,  and  5  G 
e<iual  to  thret!.     Draw  1  ,'3,  2  4. 
Finish,   noting  carefully  whore 
he  lines  of  the  jiitcher  cross  the 
<lotted  lines.     The  width  of  the 
base  of  the  jiitcher  is  equal  to 
one  part  and  a  half  of  the  verti- 
<'al  lino. 

Vakiatio-V.  —  Let  the  curve  from  1  be  unbroken 
at  f),  rounding  off  to  'A.     Make  the  outline  of  the  oi.- 

L ^  ■ 


14- 


TK.it :UKItS'    M.tM  AL. 


jinsiti!  Mi'  of  tin-  iiiti'lii'i-  till'  siuup.  Kxtt'iiil  I  L'  liiilf 
of  its  Icii^'tli  Im'voimI  2.  mill  IVom  its  i-xtn-inity  diuw 
u  stniit,'lit  line  \i.  :i  i.nii.t  just  uIm.v.'  C.  Tliis  lust  lino 
forms  tli(!  outer  line  of  tlu'  liiUiilii',  to  wliifli  uilil  tin- 
tliii'kiu'ss;  tlii'ii  j.iit   ii  spoilt,  fiirviii;,'  aliovc  llie  li-ft 

liiilfof  1  li.  iUid  imssiii;,'  tliroiiyli    its   I'l'iitn-    1 i-atli 

the  ri^lif  'lidf,  l»iit  turning  up  umiin  to  wluTi-  tlic 
liiindli'  starts. 

A  ik'sign  must  vary  somt'wliat  aii'onliiig  to  tin- 
matt-rial  from  wliicli  tin-  oliject  is  to  In-  niail',  as  silver, 
.lay,  wooil,  stoiM',  cast  or  wrought  iron. 

Cakd-Kxrkcisk  XXII. 

A  Water-Bottle  of  Simple  Curves  and  Stralnht  Lines. 

Draw  the  vertical  line  1  2,  and  divide  it  into 
fourths.  Just  aliove  the  lower 
extremity,  draw  .'»  4  equal  to 
three-l'onrtlis  of  I  -'.  Draw  the 
neck  and  stopiier,  which  occupy 
the  upper  half  of  1  2,  nuihing 
the  width  of  the  neck  eipial  to 
two-thirds  of  1  '-'.  On  the  low- 
er half  of  the  vertical  line,  draw 
simjile  curves,  forming  the  out- 
line of  the  hotly  of  the  liottle, 

as  shown  in  the  copy.     Draw  the  curves  springing 
j     from  3  and  4.     Finish. 
i         In  England  the  water-bottle  is  ipiite  extensively 

used  in  the  sleeping-rooms  of  hotels  and  in  private 

houses.     It  will  he  .seen  that  water  put  into  it  must 

of  necessity  he  kept  pure. 


rUAVTlL'AL   /»•>/'.•  .V. 


U!) 


Kxt.'iid  1  L'  liiilf 
fxtrcinity  dniw 
.  Tliis  liiHt  liii.' 
II  wliii'li  iidtl  tlit> 
^  al'ovc  tlie  li't't 

I'Clltrc     Id'lli'lltll 

II    to  wlicrt'    llif 

u'ciinlinj;  ti>  tlic 
If  iiiiidi',  us  silvtM'. 
)ii. 

II. 

1  StraiRht  Lines. 

il  divide  it  iiitii 
aliovf  tilt'  lower 
iw  .">  4  equal  to 
if  1  2.  Draw  the 
per,  wliidi  oceiipy 
If  of  1  2,  inaUint,' 
:lie  neck  eiiual  to 
1  '_'.  On  the  low- 
verticid  line,  draw 
,  forniinf?  the  out- 
udy  <»f  the  hottle, 
cnrvos  .s])rin^'in<,' 


Candleitiok,  Candle,  and  Eztingui«her. 

Draw  the  central  vertical  line,  aud  divide  it  into 
foureiinal  piirts.  'riiroii;;h  tin' 
lower  jioint  of  division,  dniw 
1  'J  a  little  longer  tliiin  three- 
foiirtlis  of  till-  vertical  line,  and 
extending  to  the  sann'  distance 
on  each  side  of  it.  >rake  .'5  4 
ei|iial  to  one-half  of  1  2.  The 
top  of  the  socket  reaches  to  the 
centre  of  the  Vertical  line,  while 
the  wick  occupies  the  upper 
half  of  the  upper  fourth.  Uraw  the  curves  care- 
fiiilv,  most  of  them  lieinj,'  compound.  I^raw  tlie 
outer  curve  of  the  handle  iiefore  drawing  the  inner. 
See  that  thi'  sides  of  the  extinguisher  have  the  same 
slope.  In  this  exercise  hut  few  exact  ineasiirenieiits 
are  given:  it  will,  therefore,  he  a  good  one  for  the 
liest  pupils  to  draw  on  the  Idackhoard  from  tin-   hook. 


QcKsrioNs.  —  Wliat  is  Miiii  of  I'onvciuioniili/.i  il  r(irn>  ' 
Wlioii  is  it  |)ro|inr  to  imitate  Niitiirc  exncily  !  Wlmt  is  mm- 
tioiioil  as  tlif  first  step  in  original  iloicri  >  How  c:iii  tlif  \<i)\\n 
of  repetition  in  numliers  on  form  he  iliuslniteil  ?  H<nv  far  is  it 
liroper  to  use  the  lilacklMianl  i  Why  -hdiilil  piijiils  in  a  ilass 
never  'Iraw  from  wall  eliarts  f 


quite  extensively 
'Is  and  in  jirivate 
r  put  into  it  niu.st 


US' 


CHAPTER  VIII. 
PRACTICAL  DKSION'. 
Fruit,  Compound  Ij«av«»,  and  Sprigi,  Conventionalised. 
The  pupils  Imve  now  leiirneil  what  in  incdiit  by 
convoiitionalized  natural  forms.  To  this  mtinncr  of 
rendering  natural  forms  for  practical  purposes,  no 
limit  can  bo  fixed.  As  there  are  different  degrees  of 
beauty  among  natural  objects,  those  objects  hIkmiM 
evidently  be  chosen  for  the  purposes  of  ornament  whidi 
will,  in  the  first  place,  afford  the  most  pleasing  effect, 
and,  in  the  aecoml  place,  will  bo  best  adapted  to  the 
particular  purpose  for  which  they  have  been  selected. 
In  one  instance  it  will  be  a  flower,  in  another  a  sprig, 
in  another  a  vine,  and  again  it  will  be  something 
else.  Thus  a  design  for  a  wall  paper,  to  be  viewed 
only  from  one  jjosition,  may  be  made  quite  different 
from  a  design  for  a  carpet,  to  be  viewed  from  all  sides. 
The  view  should  always  be  agreeable,  but  cannot  be 
if  the  design  is  seen  invertetl.  Position,  therefore,  is 
to  bo  considered ;  the  floor  and  ceiling,  for  example, 
are  to  be  distiiiL'uished  from  the  walla  of  the  room. 
Regard  nnist  also  be  jiaid  to  shape,  and  the  ornament 
be  modified  for  brackets,  corner-pieces,  finials,  corbels, 
mouldings,  columns.  Again,  no  design  is  good  that 
violates  the  .sense  of  fitness ;  construction  must  never 
be  adapted  to  ornament,  Ijut  always  ornament  to  coii- 
strnctioi).  —  to  the  object  and  its  use. 


\m 


/•NAvrii'M.  i)t:sins. 


ir.i 


ir«ntion»liaecl. 

is  mi'diit  by 
lis  maiiiuT  of 

purposes,  ni> 
3nt  degrees  of 
L)l)j('('t9  hIiouIiI 
•niiinentwli  it'll 
(leiisiiig  ett't'ct, 
ndaptetl  to  the 
been  selected, 
uotlier  a  sprij;. 
be  sometliiii^,' 
,  to  be  viewed 
iliiite  diftereiit 
from  all  sides, 
but  cannot  be 
n.  tberefore,  is 
;,  for  example. 
*  of  the  room. 
,  the  ornament 
finials,  eorl)els. 
I  is  good  that 
ion  must  never 
lament  to  con- 


<  'AKn-KxKU<'IHK    X  X  H  I. 

Aoorn  and  Cupi  OonventionalUed. 
Draw  a  vertical  line,  and  divide  it  into  three  equal 
parts.  Through  the  upper 
point  of  division,  draw  1  - 
slightly  longer  than  one-third 
of  the  vertical  line.  Above 
this,  draw  the  outline  of  the 
acorn ;  below  it,  draw  its  cup, 
de.scending  nearly  to  the  sec- 
ond point  of  division  on  the 
vertical  line.  The  outline  of 
the  cup  is  a  semi-circle.  .\dd 
the  empty  cups,  making  them  like  the  full  cup. 

Variations.  —  Draw  the  figure  as  given  in  the 
copy;  then  fill  the  sida  cups  with  acorns  of  the  same 
sliapo  aa  the  acorn  in  the  upper  cup, 

Card-Kxkkoise  XXIV. 
Aooms  and  Iieavea  Coaventionaliaad. 
Draw  the  ac(U'n»  as  in  the 
last  exercise,  and  then  ••ontiniie 
the  central  vertical  line  down- 
wards until  its  length  is 
doubled.  Draw  two  oak-leaves 
springing  symmetrically  up- 
wards from  the  bottom  of  the 
vertical  line,  and  touching  the 
sides  of  the  acorns.  There  arc 
different  varieties  of  the  oak- 
tree,  and  of  course  tney  have  leaves  somewhat  different 


l.VJ 
ill  tnrin 


rh:.ic/iKns'  mamai. 


1 1'  it  oiiii  l>i'  tloiic,  rn|Uc.-»t  tlw  piipiln  to 
l.riiiK'  ill  woiiK-  <i!ik-li'iiVL'H,  ulxo  iiooriiH,  iitiil  fmnimro 
tlu'iii  witli  till'  w\>y. 

('Altl)-KxRIUISK  XXV. 
Olover-IiOftf  Uonventlonaliaed. 
Draw  a  viTticul  liiK'  ami  liiilvc  it.  On  tin-  iiiiptT 
liaif,  as  ii  iiiiilril',  <li"a\v  tlic  t<i|( 
lolic.  I'roiii  a  point  jimt  liclow 
llic  liasr  <if  tin-  top  lolu'.  draw 
tin-  iiiiilriliH  of  tlic  luwiT  \it\n-y, 
Coniiilcti'  ^lio  lolti'S. 


Vaisiations.  —  l>ni\v       an 

(•(|iiilatcriil    ti-iaii}.;l(',  .and    from 

ha  (ciitn!  ilraw  a  straij^bt  lino 

to  carli  aii!.?lf.      On   tlic.-c   Hiicm 

V   .■oinpoiinil  leaf  like   tin-  one   in 


(llilNV 


as    iiiiih'ili 
tlu'copy. 

Draw  two  stvai;,'lit  liiit-s  bisecting  •■aclj  other  at 
ri<,'lit  aii},'l('s.  Divide  oaeli  into  tliiids,  and.  tliroii>,'li 
tlie  points  of  division  nearest  tlie  coininoii  centre  of 
tlie  two  lines,  draw  a  cirele.  On  each  of  the  outer 
parts  of  the  lines,  draw  a  single  lohe  of  the  elover-leat\ 
thus  ohtainini,'  the  etVeet  of  the  four-leaved  sham- 
rock. 

A<,'aiii.  ilraw  two  eipial  lines,  one  horizontal,  the 
other  vertical,  hiseetinj,'  each  other.  Divide  each  into 
four  eipial  parts.  On  the  upper  half  of  the  vertical 
line,  draw  a  complete  clover  leaf  pointing  upwards; 
on  tlie  lower  lialf,  draw  a  seeond  pointing  downwards. 


I'lt.wiicAi.  hksiux. 


\:i\ 


\i'   |nii»iln    to 
ad  i'oin|)aru 


Iniw  tlic  t<i|i 

it  jllKt  Ih'Iow 

>|)  1()ln'.  ilniw 

loWlT  IoIpCS. 


■  l>rii\v  ;iii 
(',  .iiiiil  tVuin 
straight  lino 
1  tlic^f   lini'H 

■  till-  one   in 

icli  other  at 
and.  thron<,di 

nil    cclltri'   of 

of  tin-  outer 
le  eliiver-leaf, 
eaved    sliaiii- 

irizontal,  thn 
ide  eaeh  into 
f  tlie  vertieal 
ng  upwards ; 
I  downwards. 


Oil  e;irli  eiel  ..f  tile  horizontal  line,  di'aw  a  single  lol.e 
of   till)  leaf.       The   re.<llit  will   lie  a  i|liatle-foil. 

('ai!I)-Kvi:ii<  i-K  NWI. 
A.  OonvontlonallaedUumpound  Iieal. 

Draw  tlio  vertieal  line  forniing  ihe  nu'liis  of  the 
I'lif,  and  tile  olilii|iie  niidrih'i 
of  the  leallels.  'riieii  di;r. 
the  uiltline  of  eaeh  leath  t. 

When  the  leaflets   of  a   eoli- 
poiind   leaf  are  sniootli-edge.'. 
draw  eaeh  eonndete,  as   show  i 
I13'    the    dotted    parts     in    tl.  • 
eopy,     .Afterwards    erase     tli  • 
parts    wliii'h    aie     not     vi-ilih. 
Visilile  parts  will  thns  he  nnel 
consistent   with  one  another,  whieh  is   not   olten   iji 
ease  unless  the  whole  form    is    drawn.      It    is   nl-i 
the    most   expeditious  met  hod,   reipiiriii^,'  the    fewe- 
eorreetions. 

Vai!1.\tio\s.  —  With  llo'  same  |iroportioiis.  laehi  . 
and  iiiidrihs,  vary  th.'  lignre  hy  giving  to  eaeh  lealh  ; 

threelol.es.  as  in  the  trefoil   leaf.     The  top  leatlet    lliaV 

I.e  oinittecl,  and  a  llower  put  in  its  place.  The  potato 
tlower  will  suit  the  jcaf  hest. 

.\gain,  draw  two  straight  lines  Kisecting  each  oile:' 
at  right  angles.     On  this  cross,  draw   four  coniiMHind 

leaves,  lihe  tl lie  given  ill  the  coj>y.       I'.et weell  each 

pair,  draw  a  cin.pie-roi!  tlower,  that  is.  a  llower  having 
live  leaver  ;  or  draw  a  hiiiwli  of  spheres  which  shall 
represent   tlu'  hall  of  s I  of  the  llower. 


ITti  TKAVIIKNS'    W.I.V/  .1/-. 

CAiii»-KxKK«;iHK  XXVII. 

Wina-Olui. 

ICuvinpf  <livi<l«'il  the  Vfrtiful  line  into  four  otiuul 
parts,  iiiuki-  1  '2,  H  t,  <>(|nul  to 
two  of  tlu»»c  i»iirtH,  r»  (1  to  one 
of  tlio  purtit,  uiiil  7  <S  II  liltlii 
HliorttT  tiniii  ') «).  Druw  in  this 
ortlur:  Itowl.  !ttt>tn,  hiwe, 

Vakiations.  —  With  tlif 
Kunu)  proportional  divistion  of 
tli(>  vertical  lint-  ii  gn-ut  variety 
of  Mliupes  iniiy  bo  ohtiiiiit'<l. 
riniH,  mako  1  H,  2  fi,  Htrninlit, 
and  tliu  Htuui  plain. 

Agiiin,  ImvinK  drawn  1  5,  2  6,  HtraiRlit,  uhh  tliom  aH 
fonntrjction  linen,  lialving  tlicm,  anil  throii^li  tlio 
points  of  (livirtion  drawing  compound  cnrves  to  form 
the  protilc  of  tlie  ImiwI.  In  tin-  ciMitri'  of  the  utoni, 
draw  a  circle  with  a  diameter  one-eighth  of  the  verti- 
cal line.  HaHc  of  glas.s  the  Hume  in  the  thr'-e  ca«e>*. 
Draw  parallel  horizontal  donhh'  lines  near  the  lip.  and 
lictweeii  them  draw  a  star  repi-ated  around  the  glass. 
Tile  star  may  \m  composed  of  four  straight  lines  cros.s- 
iiig  one  another  at  a  common  centre,  the  alternate 
lines  mutually  perpeiidicidar. 

See  that  the  pupils,  when  they  examine  their  draw- 
ings, do  not  look  at  them  oldiiindy.  They  should 
holil  them  directly  in  front  of  the  eye,  and  turn  them 
around.  I'liless  rrcipiently  reminded,  they  will  neglect 
to  do  this. 


f'N.ivw.n.  hhsnis. 


IM 


>   four  <Mitiikl 

1  i,  *'(|liul     to 

I,  5  Ti  til  oiitt 
7  )H  II  liltlo 
Druw  in  thin 

-  With     tli.' 

tliviHioi)    oi' 

grt'iit  viirifty 

bo    olttiiiin'il. 

2  (\,  Htrnight, 

,  UHtt  tllOm  IIH 

throu^li   tlie 

rvfs  to  form 

(if  tlw  (ttoni, 

of  tlu<  VlTti- 

tlir''t'  cn^cfi. 

ir  tlic  lip,  iiiiil 

11(1  till'   k'"*"'' 

lit  liIH'^«^'r()»»- 

tlif   uUcniiito 

H-  their (Iraw- 

Tlicy  ?*h(nilil 

11(1  turn  them 

•y  will  ni'j^Icrt 


<;AUI.-KsMt!l«K    XXVIII 
A  Mouldlna  of  H«ftrtib«p«d  Zi«*TM. 

Uriiw  II  Hfjiiuro  tiiul  itH  viTticiil  diimictfr.  TlirouKli 
II  point  li  little  hi'low  the  een- 
tro  of  thiit  (liaincter,  ilruw  ii 
hori/.ontitl  line  iiidiciitin^  th'« 
Uri'iiteNt  breiulth  of  the  leaf. 
Draw  tho  coni|ioun<l  eiirvoii 
tiH  in  tho  copy.  Next,  divido 
the  lower  niihf  of  the  H(|uart> 
into  foiirei|uiil  parts;  on  each 
part,  coniitruct  a  nquare,  and 
till  it  iiH  the  larm*  xcjuare  wan 

tuh-a. 

CAHn-KXKRf!I«K    XXIX. 
AMU*. 
Draw  the  central  vertical  line,  und  divide  it  into  six 
eijuai    partH.      Make    1  'J,   3  4, 
equal  to  two-thirds   of  the  ver- 
tical  line,  imd   draw    the   sides 
ot"  the  iiiu^.      Draw   the    hori- 
zontal lines,  the  lower  one    of 
the   upper    group  through    the 
upper  point   of  division  on   the 
vertical  line,  tho  upper  ono  of 
tilt!   lower    group   through    the 
lower  point  of  division,  and  tlie 
single  one  through  the  central  point  of  division.     <H>- 
servo  that  the  tlutings  towards  the  hottoin  <h'creaso  in 
width    t.i    right   and   left.  Ihmiiusc    tliev  are    seen    oli- 


\M 


n:  \i  iihHs'  Mtsr.it. 


liiiMi'lv-  Mi^l*)'  'ill'  llltll'lli'  lit  itn  t«ii|i'>t  )i>ii>|i  i'i|iiill 
to  'HM-lllll'l  <ini!»'  V>rl«rill   lillf,  Willi  itp«  Kr»'(l»t'»t  [ifo- 

jiM-iloii  fruni  !!»<•  ui»\i  inwanU  tlii>  top.  Notice  tli«- 
liMii/.i.iituI  Wui'*  Irfin  wliivli  I|»k  lmn<lli'  (•(•rimt"- 
Ihiiw  lii«l  till-  iiihi'i'  lillf,  wliii  li  nivfi  tin-  tliiiltin** 
of  till'  liiiinllt'.  l'.i|)iU  iiu'liiii'  to  iiiaki'  iIm>  liuuill<' 
tliii'lc  ami  I'liiiiiity.     ,\iitii<i|Mitu  nnil  |iri>vi'hl  tliiM, 

N'viiuilov.  —  Divi'lf  tlti- ichtrul  vi'i'tirtil  !int<  iiiln 
(|iiitrtcrH,  uikI  iitaki'  llh>  wi'tili  <A'  the  iiniu  i'<|iiiil  t** 
liulf  itd  liciKltt.  Ki'i'|>  llii>  littler  lii'tiiitM  tlio  xitiiH', 
hilt  iiiii'<t<  tlio  liiiiiilli'  liiill'  N<|iiiirt'  III  ■«liii|ic,  ]i)'iiji'<'fiii^r 
an  Wit  im  ill  tin*  rupy,  uiul  i'i|ii»lly  nt  top   iiiitl    li>it|iiiii. 


t'vuii-KxKiM  iMi:  XXX. 

MAple-Lvitr  UonvcntloDnIlsed. 

I^raw  u  vi'i'fii'Ml  liin'.  un<l  iliviili*  it  iiitu  fliinl-*.  Miil<i' 
I  -  i(jMiil  til  twii-tliinU  of 
ilio  virlir;il  line.  |>ivi<li'  I 
w     into    tliinU.    ami,    tliroii^li 


llio    pointM 


ilivi^iuii 

-iilo 


ilruw 

lllrt  VfillH  of  till'  >i(li'  IiiIm'K. 
Coiiipliti'  till'  Ii'iil'  iiH  hlmwii. 
XotiiM!  timt  fli>'  I'lirvcM  vvltlirll 
cllflosi'  till'  liilx-f*  of  tlir  Ii'llf 
iihviiVH  luiiil  oiitwanlM  rrmii  tin- 
iHMitroof  till*  IoIh' ;  alsotliat  tin- 
tint's  at  lilt'  jiiiiftioii  of  tlio  loht'n  iiowlitTi'  form  uii- 
)j;lt'x  hilt  Inivi'  a  roiiinlt'il  Hliupi'.  Ut'iiirirf  tins  piijiiN 
to  (iriiw  this  ]c;if  ri'i.ni  tiiiif  to  tiiiii",  until  tlu'v  i-aii 
riiniilv  ilraw  it  iV.oii  iiK-iuorv. 


i'MACnCil.  hUf'lUS. 


IW 


N«iti<'<'  titi 
r'lli'     »|>riiiK«. 

till'     lllll  tilK  ■'I 
•     tllK      llUtllilc 

t*lit  tliim. 

irul  lino  iiilo 

I*     till)     Mttltll', 

|M-,  |tfiijt'rlillg 

iiimI    I'otloiii, 


fliinl-*.  MitUc 
\vo-tliinlf«  of 
hivi)li>  I 
mil,  tlit'oii^'li 
ivi'^ioii.   ili'iiw 

if  (IS  »li(ivvii. 
I'lirvcH  witicli 

iif  till-  li'iii 
mix  IViiiii  till' 

rtlso  tliiit  tin- 
icri'  form  jiii- 
re  tlu!  |iiii>iN 
litil    tlii'v  rail 


OAHIi-KXKHriHK    XXXI. 

Uriiw  u  li.iriftiiitiil  un.l  h  xiIi.uI  liiii<  of  tin-  unni" 
yiviMi  liii(;lli,  liiitf<Jiii«  ••ikIi 
••titer.  I>iviit<>  I'Kfh  ill* 
tU'wU  I'liitf  till'  ixdhtu 
•if  ilivinioii,  tliiu  foriiiiiit;  n 
i«|ii;ih-  oil  ItM  tliii^oiiiilK. 
Witliiii  till'  itt|imrf,  ilruw  ii 
tri'foil  ;  witliiii  tin-  tn  f'lil.  ii 
iiirvi'<l  i><|iiil;tti'iiil  triaiiKl''. 
Oil  till-  oiltfr  lliil'ii  of  tin 
viTtirul    uiul  li)iri«»iit>il    liiit'x, 

.Iniw vi'Utiiiuiilizi'il  muplt-lfiivi  ■>,  li.iviiiK  slir  |>i"- 

|iiirtiiMiiinuUlii«iK>(i|  iliiMiiiu  ill  tli«-  Uwt  ainl-txi'wiM'. 

C'AKi»-KxKHrii*»',  XXXll. 
OonTei>Uon»li«ed  rorm ;  Simple  LeaVM  MJd  Flow^ri. 
l>iii\v  till'  \.  itiral  liii"  I  Ii,  iK'*l  (livido   it   into   four 

i'i|iiiii  j>;iit^.     .Muiii'  .">  I.  r»  0, 

ciiiiiil  tu  oiit-liuH  of  till'  verti- 
cal liMf.  •">  >  to  Ih!  ilravvii 
tliriMi)fli  tln'  iippi-r  point  of 
ilivjoion  oil  till*  vcrtiiiil  line 
Draw  llr^t  tlii>  iiii'lrilis  luul 
!<ti>iii!S  of  tin-  liMVi-.t,  mid  th«>ti 
tlii'ir  iu;tt'i,'iii».  I  >i':uv  tin-  llowvr 
lit  tliii  to|>,  uimI  lastly  till-  littlv 
tiri'li'.H  at  till"  Itottoin.  rfpri'Sfnt- 
•iij;  till'  lit'rricK. 


M 


i  m 


TKdVIIIHHI'  Mi, MAI. 


Cudi-KKKNi  Mr.  XX Mil. 
0<in*«nUon«lls«<i  rorm.    l'r«roit  !.«•»••  Mid  flowMt. 

|)riiw  It  vt  vtii'til  linn  ol'  lUiy  Kivfii  Ifiigtli,  uixl  ili>i«l<' 
It  into  lliinU.     Muk«>  t  'J  ami 

.'(  t  iMlHitl  to,  iMIil  TlO  a  little  ji-M 

tlutii,  tMi)-tliir<lii  cit  till'  vrrtit'iil 
liiti*.  Connttt  .')  R  anil  4  *l. 
Kroni  till'  I'mln  i4'  •14.  ilmw  tlii< 
loiiK  riirv«'H,  giving  tin-  I'l'ii- 
Iri'i  of  till'  two  li'ikvi'n  anil 
-III  Krotii  tin-  •iiiU  of  1  i, 

lit  iw  till'  ri)ni|ioiiiiil  nirvt'ii 
wliii'li  form  till'  oiitliiii-  of  tlin 
flowirx.  Tlii'Ki'  lUirvi'H,  iiftir  toiuliiiiK  .'I  4  ut  a  »liort 
tlinfaui'i'  frtnn  tlm  v«'rtii'ul  lim',  turn  upwanU.  uml  iiiiito 
oil  till'  virtual  liiii'  oiii-tliinl  of  tlu'  wiiy  froni  M  4  to 
I  li.  Uraw  till'  utriii  III  till'  llowtT  lioiii  tin'  |ioiiit« 
wliirt'  il»  ontliiM'  foiiilu'ii  .'I  4.  Ailil,  Ity  nH-iwuriMiunt 
of  «'y<',  till'  liitailx  of  till*  flowiT,  Icavoii,  uml  |K'nilt'nt 
ln'rrii''«. 


Qi'MTIrtNi.  — WImt  l»  »i»lil  of  the  liiiiil  III  lonvtiitloimlizi'l 
iiittiiiiil  lonn-> '  By  wliiit  iiii'  you  to  Ih-  kuIiIiiI  in  KiUctiiiK  ilil- 
(■(•niil  lurmi*  lur  tin'  |iiir|ioi<i'«  ul  orniiniiiitiitijii  I  How  nIiduIiI 
nrmuni'iii  Iw  iiitlmiuril  liv  |u)iitlon  *     Uy  »liu|>i'  I     By  u»i' ' 


1(1  Flowari, 

I,  utui  <tivt)i«> 
itki'  t  '.'  nml 

I  n   little    ll'KM 

till'    VrrticttI 

A  anil  4  «t. 
II  t.  ilmw  l)i« 

Ig     tllf      CI'll- 
It'lkVt'ii      lUlit 

fiiiU  of  1  '2, 

iiiiitl     ctirvfrt 

lltlllM-    t)l'    till' 

■I  ikt  a  r  liort 
rti»,  itinl  iiiiiti) 
,  IVitiii  M  4  to 

II  till'  poilltrt 
iiH'iirtiiri'iiU'iit 

llllll     |H>lllll'llt 


.'UllVl'lltlullull/Cll 

ill  M'U'ctiiiK  ilil- 
I  lluw  nIiiiuIiI 
I     Hy  u»i.' ' 


«'HAI'TKU  IX, 

KOHMM  OK  I.KAVKM   AND   I'LOWKIW. 

uTimV    'tf    MnTAMV. 

1 1   liii-  ulri'U'ly  l'i'«'ii  nftlil,  tliut  Niitiir««  oftt-ii  ImiUU 

ii|Miii  iiitirki'il   gi'iiiiH'trii'tkl   i'oniiK.      In  il<<taiU  mIi«>  ii* 

f     irri'ttnlttr,  Imt  umiully  tin'  ri'ViTwi  in  d^fiu'rul  uiitliiik'.!. 

'I'llllt    tllim    U    trill'    of  li'UVi'*    UlliI  (loWlTi,   will  III-  Nl't'll 

I'rniii  till' I'Xi'rrini'fi  wliirli  miiiH'iliiiti'ly  full'iw.  Aiiimin 
li'tivii«,  notiiK  liuM'  till-  t(i'iii'rikl  fiiriii  tif  till'  I'llijwi', 
iitlu'rw  of  tln'  •iviil,  otliiTM  of  till'  Iriuiiuli'.  wliili'  oiIhtk 

liri'     llUull'llnl     M|M>ll     till'     |H'lltllJ{oll.         AlllollK     (loWI'fK, 

■      iliiTi'  ii  II  Ic -s  viiriity  of  I'oniid,  niiici'    tlnir  jii'tiilH   uri' 
imiiully  iirriiiiKi'i'  nyiniiu'trii'iilly  unMiinl  u  I'l'iiti'ii, 

i  |{ii|iii'st  iiuli  |iii|iil   {<>   \>r\\ni   I"   Hrliool    till'    li'uf  of 

{      uiiy  iii'»i«iiiiti'il   till',   xlinili,  llowiT :   u-.    tlir   iiiii|ili'. 
roKi',  lily.     Kii'li  |miiil  liiiviiij?  in   liin  IuuhI   iln'   "n"'" 
I      viirii'ty  of  Itiuf,  pmci'i'il  to  yivf  u  h-nnoii  mi    itn    form 
I      ami  Hlriifturi',  toai'liiiin  lit  tin'  hiiiiii<  tiiiu'  liotli  lioluiiy 
iiinl  till'  iniiirilili'H  of  piin'ticul  ili'^in'i-      I'or  ii  »ri'oiii| 
!      lt>«Muii,  tttk't  tint  muno  U'lif,  Ixit  mill  luiotlior,  uinl  ti-mli 
till'  impilrt  to  <oin|iiir(»  tlic  two.     TIiiih  proii'i'd  from 
oni!  Ii'tif  ivnil   tloMiT  to  luiotlicr,  iiinl  iit  hist   ri'i|uii" 
I'ucli    iiiiitil   to   liriiiK   to   Hfliool    tlio   liirgi'st    |iohhil(li) 
iiiiinbiT  of  ilifffrunt    li'iivud,  ami    iiKnin    of   tlowurn. 
Tiiis   work   hIiouKI,   of  fourm',   »v   iloim   at    tin-   most 
fuvorahli'  huuboii  of  tint  yi'ur. 

Acnuaint    the   pupiU  with    tho    proju'r    botanical 


nil  I 


TEAVIIEUS'    MAM  AL 


l.Tins.     Till-  iolldwiiif,'  iivc   S..111I'  of  the  terms   it  will 

Ik!  iicci'ssiiry  ti)   iim- ;  ntlicrs  ciin  In-   vfiidily  obtiiiiictl 

from  liny  good  work  on  liotiiiiy.  if  you  urc  not  ivlrcaily 

muster  of  tlie   snlijeel,   us  every   teaelier  of  eliihlren 

slioiiM  lie. 

I'ktioi.i;— Tills  is  tlic  lenfsiom,  or  lonf-stiilk. 

MiDiuii  —  Till'*  is  till- I'ontiiiiiiuion  ol  tlic  jii'tiolo,  ivii(\  lonns 

I  lit"  iixis  of  the  li'iil. 

Hilis,  _  Wiicii  the  iK'tiolc  divides,  us  it  does  in  llie  iim|)lc-lci\f, 
eiicli  of  tlic  ilivisions  is,  ertllcd  ii  ril),     Tliere  is  liieii  no  inidrib. 

ViiiNs  —  Tliese  luv  tlie  smiili  hninelies  wiiicli   )mt   out  fiom 

llir  iiiidi  iii,  <ir  tVoiii  tlie  ribs. 

Vkim.kth.  —  Tiiese  are  smiili  Imimdies  imttiii};  out  lioin  tliu 

veins. 
Hum:  —  Tliis  is  tlie  liroad,  Hut  part  of  tiie  leaf. 
A'i;NVTlos.—Tiie  lines  seen  upon  tlic  Idaile  eonstiiute  what 

is  ealled  iis  venation. 

Mauoin.  — This  is  the  ed;:e  of  the  leaf.  It  may  he  entire, 
that  is,  unbroken,  as  with  the  lilae  ;  it  may  be  serrate,  haviiif: 
sharp  notches,  ns  with  the  syriuga;  it  may  he  erenate,  havinj; 
broad,  round  notehes,  as  with  the  eatnii.-leaf.  There  me  many 
other  varieties. 

A  LoiiKl)  Lf.AK.  — When  the  notehes  in  the  niar^'in  ot  a 
leaf  niv  deep,  as  with  the  oak  and  maple,  the  leaf  i«  said  to  be 
lobed.     The  deep  notehes  are  enlled  sinuses. 

lUsB  AND  Ai-K.\.  — The  iiart  of  the  blade  next  the  jK'tiolc 
is  ealled  the  base  of  the  leaf;  the  opposite  part  is  .-ailed  the 
npex.  These  lov  of  all  shajies,  as  eordate,  or  heart-shaped  ; 
hastate,  or  si)earsha|)ed  ;  aeute,  or  sharp;  obtuse,  or  blunt ;  and 

so  on. 

CoMi'oiiNK  Leaf.  —  This  consists  (,f  .several  leaves,  or  rather 
leaflets,  attaihed  to  a  eominon  raehis,  as  in  the  rose-leaf. 

1{  uiiis  —  This  is  the  continuation  of  the  jictiole,  or  stalk,  to 
whieh  the  leaflets  of  a  compound  leaf,  or  to  which  the  stems  of 
a  cluster  o*'  flowers,  arc  attached. 

I'icDtxci.E.  — This  is  the  flower-stalk  of  a  single  flower  or 
the  raihis  of  n  cluster  of  flowers. 


terms  It  will 
idily  obtiiiiM'il 
•('  not  ulrciuly 
■r  of  cliildrt'ii 


■tioii',  and  roniis      | 

i 

n  tlu'  iiiuplc-lcnf,      | 

licM  110  niiilrili. 

ii   |iiit   out  IVnm      I 

II};  out  IViiin  tlio      j 

k'lif.  i 

c  I'oiistiiuto  wlint      I 

! 

it  limy  he  I'litiiv, 
L-  seirato,  Imviii;: 
i  CTcimtc,  liuviii;; 
TIr'ic  mv  miiiiy 

the  iiiiui;iii  ut'  « 
cal'  i<  saiil  to  lio 

•  ni'Xt  tlie  jK'tiole      , 
uirt  is  calk'cl  tlie 
or  hi'art-sliiiiied  ; 
ISO,  or  blutit ;  and      i 

il  leaves,  or  rather  j 

rose-loaf.  | 

ctiole,  or  stalk,  to  i 

liicli  the  stems  of  | 

I  single  tlower  or 


FOKMS  OF  LKAVKS  ANh   FLOWEHS. 


nil 


('ai.vx.  —  This  is  the  i'ii]i,  or  oiitrr  circli',  ui  lnivr>.  wliiih 
lii'loti);  to  a  flower. 

Hki'AL.  —  This  is  one  of  the  leaves  lomposlii;,'  tlic  enlvx. 

(^oitoi.i.A. — This  consists  of  the  usually  dclicatilv  ruloird 
(lower-leaves  inside  the  ealyx. 

I'lCTALS.  —  These  are  leaves  of  tint  eondla. 

SrAMKNS.  —  These  are  the  sli'iidcr  parts  toiind  next  iiisidi' 
the  eoi'olla. 

I'iRTIl,.  —  This  is  the  central  jiurt  of  ilic  llower  wiiliin  the 
HtHinens. 

F1.0WKU  IN  I'l.AN  ANI>  Kl.KVATlON.  —  The  first  is  the  llower 
as  seen  when  vi^  rd  directly  from  ahovc ;  the  second  iis  seen 
when  it  is  viewed  from  ono  side. 


Caku-Kxkkcisk  XXXTV. 
Syringa-IJeaf  slifttitly  Conventionalized. 

Draw  a.  verticiil  lino  forming  tlio  midrib  offlio  Innf. 
and  dividt!  it  into  fivo  equal 
ptirts.  Tiirotigh'  tliti  second 
point  of  divi.sion  from  tlie  bot- 
tom, draw  a  horizontal  line 
ono-lialf  iis  long  as  the  verticil 
line.  Add  the  veins  joining 
the  midrib.  Around  the  whole, 
draw  the  .serrate  margin  of  the 
leaf.  The  apex  of  th(!  leaf  is 
acuminate ;  the  base  obtuse. 
The  whole  leaf  is  slightly  con- 
ventionalized, making  it  symmetrical.  As  a  whole, 
the  leaf  is  oval,  inclining  to  the  ellipse. 

With  the  proportions  thus  given,  the  pupils  can 
readily  draw  the  leaf  many  times  larger  than  in  the 
copy. 


14* 


U\-l 


Tt:.{riih:/,'s'   MAS'C.l/.. 


Cakd-Kxkhcihk  XXXV. 
OatniP'Iieaf,  allKhtly  Conv«ntionallied. 

Draw  ii  viTticivl  liiiu  t'ormiii^  tlit!  miilril)  iiml  potiolo 
of  tlio  leaf,  and  iliviilo  it  into 
thirds.  Throiigli  the  lowi-r 
point  of  division,  draw  a  hori- 
zontal lino  two-thirds  as  lon^ 
as  the  vertical  lint!.  Add  tlm 
veins.  Around  the  whole, 
draw  tho  i-ronati-  margin  of 
the  leaf.  Thu  base  of  the 
leaf  is  cordate,  or  lieart- 
^■^■^■^■■■■^■B  shaped  ;  its  apex  itcttte.  .'he 
I  petiole,  or  leaf-stalk,  occupies  one-half  of  the  lower 
i     third  of  th(!  vertical  line.     As  a  whole,  th.'  leaf  is  de- 

i     cidely  oval. 
i 

Cakd-K-kkucisk  XXXV I. 

German  Ivy-Leaf,  sliKbtly  Conventionalized. 
Draw  a  vertical  line  forming  the  midrib  and  petiole 
of  the  leaf,  and  divide  it  into 
three  equal  parts.  Through  the 
points  of  division  and  through 
the  lower  end  of  the  line,  draw 
horizontal  lines,  tiie  upper  and 
lower  a  little  more  tiian  half, 
the  central  a  little  less  than 
half,  as  long  as  the  vertical 
line.  Add  the  side  ribs,  and, 
around  the  whole,  draw  the 
margin  of  the  leaf.     The  margin  is  .uitire  ;  the  leaf 


yOR}fli  OF  LEAVES  ASh  FUtWKHS.         Hi:i 


lied. 

>  iiiid  ])uti()l(t 
livido  it  iiitii 
I  the  lower 
,  draw  a  hori- 
lirdH  as  long 
,0.  Add  i\w 
tho  wIjoK', 
!•  margin  of 
base  of  tin.' 
,  or  lit'urt- 
afuti'.  ."111! 
uf  tlio  lower 
lie  leaf  is  de- 


lalized. 
I)  and  petiole 
livide  it  into 
Througli  the 
and  through 
he  line,  draw 
lie  uppcu'  and 
•0  than  half, 
tie  less  than 
the  vertical 
ide  ribs,  and, 
le,  draw  the 
;ire ;  the  leaf 


ftve-lobed,  with  sinuHes  very  siiallow.      As  a  whole,  the 
loaf  is  pimtagoiial. 

Cahi)-Kxkk(;isk  XXXVII. 
Ooosaberry-Leaf,  sliKhtly  Conventionaltaed. 
Draw  a  vertical  lino  forming  the  midrib  and  petiole 
of  the  leaf,  and  divide   it  into 
thirds.     Just  below  tho  upper 
point  of  division,  draw  a  hori- 
zontal lino  not  quite  as  long  iia 
tho    vertical    line.      Add    the 
other  ribs  and  tho  vein.s,  and 
around    tho    whole    draw   the 
margin  of  tho  leaf.     The  leaf 
is     five-lobed,     sinuses     deep, 
nuvrgin  unevenly  serrate. 


Cauo-Exeroisk  XXXVIII. 
Strawberry-Iieaf,  alishtly  Conventionaliaed. 
Draw  a  vertical  line  forming  the  petiole  of  the 
and  the  midrib  of  the  cen- 
tral    leaflet.      Divido    this 
line       into      thirds,     and, 
through  the  upper  point  of 
division,  draw  a  horizontal 
line  as  long  as  the  vertical 
line.     Draw  the  midribs  of 
the  right  and  left  leaflets, 
and  add   the  veins  for  all 
three.     Finish   by  drawing 
the  coarsely  serrate  margin  of  each  leaflet. 


leaf 


I — ■"" ' 

I     1U4 


TK.tVllKHS'   MANUAL. 


A  li'jnf,  sliRhtly  OonventionallEed. 
Draw  the  vertirul  lim-,  forming  tlio  midrib,  iiiitl 
(lividt*  it  into  thirds.  Just 
iibovc  tlie  centre,  draw  a  hori- 
zontal line,  making  it  eiiiial  to 
two-thirds  of  tlu'  vortical  line. 
Add  the  other  horizontal  lines, 
ont;  below  and  two  above,  by 
j udgment  of  eye.  Then  draw 
the  lines  forniinj^  the  veins, 
and,  around  their  ends,  draw 

the  margin  of  the  leaf. 

This  leaf  is  just  onouKh  conventionalized  to  make 
it  symmetri.'al.  As  it  is  a  simple  leaf,  the  midrib  is 
the  axis. 

CurraDt  Leaf,  slightly  Conventionalized. 
Hr.aw  the  vertictal  line,  forminR  the  midrib  of  the 
leaf,  and  divide  it  into  four 
e(iual  parts.  Through  tlu! 
upper  point  of  division,  draw 
the  horizontal  line,  making  it 
equal  to  three-fourths  of  tho 


vertical    line;    tlirough     th( 
lower  point  of  division,  draw 
a     second     horizontal     line, 
making  it  a  little  shorter  than 
the    first.      Add      the    lines 

forming  the  veins,  and.  around  their  ends,  draw  the 

margin  of  tl-e  pentagonal  leaf. 

Tiiis  leaf  is,  also,  just  enough  conventionalized  to 

make  it  symmetrical' on  its  midrib,  which  is  the  axis. 


FOUMS  OF  LEAVFS  A.\H   tUtWt.lls.  I 


)>o 


Bed. 

u  midrib,  iiiid 
tliirils.  diiHt 
5,  draw  ii  liori- 
ing  it  c'cjuiil  to 
«'  verticivl  line, 
orizontal  linos, 
two  above,  by 
e.  Tben  draw 
ing  tlie  veins, 
t'ir  endn,  draw 
\w  leaf. 
Uized  to  inako 
",  tlie  midrib  is 


aalized. 

midrib  of  tluf 
le   it   into  four 

Through  tlu; 
'  division,  draw 
line,  making  it 
-fourths  of  the 

through  till! 
■  division,  draw 
ori/ontal  line, 
tie  shorter  than 
dd  the  lines 
ends,  draw  tlie 

ventionalized  to 
lich  is  the  axis. 


Hawthorn-Leaf,  »llKhtly  Oonventlonallaed, 
Draw  the   vertieiii  line,  forming   the  midrib,  and 
divide  it  into  four  f(iual  parts. 
Through  the  central  point  of 
division,  draw  the  upper  hori- 
zontal line,  making  it  a  little 
longer    than    one-half  of  the 
vertical  line;  and,  through  the 
lower  point  of  division,  draw  a 
se<ond  horizontal  line,  making 
it  a  little  shorter  than  three- 
fourths   of  the    vertical    line, 
but  longer  than   the   iirst   horizontal   line.     Add  the 
lines  forming  the  veins,  and,  around  their  ends,  draw 
the  margin  of  the  leaf,  ti  ^  -liown  in  the  copy. 

This  leaf  is  not  quite  from  nature,  but  is  con- 
ventionalized just  enough  t(i  make  it  symmetrical  on 
its  midrib.     The  left  side  balances  tiie  ri;4ht. 

Oeranium-Iieaf.  Blinh'ly  Conventionalized. 

Draw  a  vertical  line.  From  a  point  jii>t  l.cli.w  liie 
centre,  draw  the  lines  forming 
the  ribs;  and,  around  these, 
draw  the  contour  of  the  leaf, 
making  the  breadth  a  tritht 
greater  than  its  height. 

Use  these  ditt'c^rent  leaves 
not  on  the  cards,  for  black- 
board lessons,  an<l  for  the 
purpose  of  giving  further  illus- 
trations of  principles  of  design, 
and  for  imparting  a  knowledge  of  botany. 


r 


Kit) 


r  EACH  Kits'   MAXl'AL 


Cakd-Kxkiuisk  XXXIX. 
Laburnum<Lear,  aliKhtly  O  jnT«ntlonalla«d. 

Drftw  ft  vertical  line,  forniiiig  tli»»  iH-tiulo  of  tlio 
lt>uf  und  tint  ini<lril>  of  tlie 
central  leaflet.  Dividt;  tln'H 
lino  into  four  ocjiial  piirtH. 
Make  tlio  nii(lril)8  of  tlio  ri^jlit 
and  left  Jcaflctn  about  two- 
tliirds  OS  long  as  tlie  niidribH 
of  the  central  leaflet.  The 
breadth  of  each  leaflet  in  a 
little  le8!i  than  one-half  uf  itn 
length.  The  margin  is  en- 
tire. This  is  a  compound  leaf,  each  leaflet  ellij)tical; 
general  outline  of  the  whole  triangular. 


Cakd-Exbrcihk  XL. 
Boae-Laaf,  illRbtljr  OonventlonallHed. 

Draw  a  vertical  line  for  the  rachia,  and  mark  the 
points  of  junction  made  by  the 
leaflets  with  it.  Draw  the 
midribs  of  the  leaflets,  and 
flnish.  Kach  leaflet  is 
elliptical:  the  whole  leaf,  in 
its  general  outline,  might  be 
called  the  same.  This  is  a 
compound  leaf,  whicli  is  quite 
a  different  thing  from  a  lobed 
leiif.  Sometimes,  however,  it 
is  no  easy  matter  to  distinguish  one  from  the  other. 


1 


FOItM.S  Of  I.K.xyhS  AM>   hUtWhllS. 


h\ 


Used. 

'tiiiUt  of  tlie 
ilril>  of  (lip 
Divido  tluH 
i|iiul  piirtH. 
of  tlio  rij,'lit 
ivliout  two- 
tlie  midribs 
t'iirtet.  Tlio 
li'iUV't  irt  a 
I'-lialf  of  it» 
rgiii  is  en- 
it  elliptical ; 


ed. 

(1  niiirk  tlio 
iniule  by  the 

l)r.aw  tlio 
eafluts,  and 
luaflct  is 
ole  h'af,  in 
i,  might  be 

This  is  a 
ich  is  quite 
om  a  lobed 
however,  it 
the  other. 


<!Aiti)-!CxKH(:isE  Mil. 
Wlld-RoMliea»e«»nd  Flowers  from  Nature, 
Ai  r(  we  iiave  the  j.lan  of  ll«<'  Hower,  or  the  flower 
a^   Heeii   when    we  look  down 
npon    it.      'rbi.-*    i"  l>«'ntaKo- 
iial,  cimiiie-foil,  or  five-leaved. 
At  li  \\A'  hiive  the  i-levation  of 
the   flower,  or  the  Hide   view. 
At  (■  we  have  the  bud;  and 
ut  (/   the  eouipound   leaf.     It 
will  he  Keen,  that  the  snaigin 
of  the  natural  leaflet   is  ser- 
rate, and  not  entire,  as  given 
in  the  last  exercise,  where  the  loaf  is  slightly  cou- 
vi'iitionali/.ed. 

Observe  how  syinnietrieally  the  live  large  jietals  of 
the  corolla  at  a,  also  the  flvo  small  petals  of  th*) 
calyx,  making  ten  in  all,  are  arranged  about  the 
centre  of  the  flower.  The  ten  little  stamens  near  the 
(^entro  have  the  same  symmetrical  arrangement. 
Observe,  also,  how  symmetrically  the  leaflets  of  the 
compound  leaf  at  d  are  arranged  on  an  axis,  that  is, 
on  the  ratOiis  from  which  the  leaflets  spring. 

As  the  i)upils  draw  tlie  leaves  and  flowers,  q\iestion 
them  about  their  forms  and  parts.  Do  this  until 
they  are  perfectly  familiar  with  the  terms  used.  At 
the  same  time  question  them,  also,  about  the  jirin- 
ciples  of  design  to  be  learned  from  these  natural 
forms.  You  can  readily  make  this  a  very  interesting 
exercise.  In  tho  same  way  .shells  and  insects  nlay 
bo  drawn,  and  lessons  in  design  learned  from  them. 


ICS 


•SHMmnUS'  MANVAL. 


(Aiiii-KxiJii'im.;   X  lill. 

Oran«'a-BIU  Flower,  Iiaaf,  ^nd  Bud  from  Natur*. 

At  a  we  liiivo  the  plan  r»f  tin-  llowi-r;  iit  l>  tlin  cli'- 
viitioii  ;  lit  (/  tlic  h'lif ;  (it 
/■  tlm  lm<l,  wlioHo  f«Im|)n  ^ivi's 
till!  iiaiiU',  —  crimi''-*  hill. 
Till'  tliiWiT  \*  |ii'iitai;niial, 
iilso  tlif  Iciit'.  Taki'  iHitirt! 
of  tlic  yyiiiiin'trii;al  arraiij^i'- 
iiii'iit  of  |M'tal!4  anil  staiiii'iis 
aliitnt  tlic  (u'litrc  of  tin-  (ii<w- 
rr  at  (/.  (Joniimrt'  tlm  It-af  at 
(/  with  till'  Iraf  at  «/  in  tlu' 
last  ranl-rxiTcisc.  This  is  ilfcjily  lohnl  and  siiii|il(', 
Nvliili'  tilt'  othir  is  coinpoiiiiil.  This  is  synwMctrirally 
lialaiiccd  on  its  ri-iitral  rih ;  that  is,  on  its  nuliis. 

For  at  Irast  a  part  of  each  yi'ur,  I'otaiiy  shmilil  hi< 
taught  in  fvi'i y  ]iriiiiarv  sihool  ;  ami  to  ii  (H-rtaiii  I'X- 
ti'iit  it  sliniilil  Im'  taught  ill  rotiiu'rtioii  with  drawing 
am!  ili'sigii':r,'.  The  reproduction  with  thi'  pencil  of 
tlic  forms  of  leaves,  hmls.  tiowcrs,  sprij^s,  vines,  ferns, 
etc..  would  not  ordy  he  good  pruciii'c  in  ilrawing, 
even  if  the  forms  were  only  conventionalized,  all  tlio 
little  details  liciiig  omitted,  hut  would  ipiiidven  the 
peice])tive  powers  much  more  than  the  mere  act  of 
nliserviiig  the  funiis  ;is  a  student  of  Hcience,  and  thus 
wmild  tlrmly  fix  the  hotaiiical  Ijiiowledge  in  the 
mind.  And,  then,  the  study  of  the  manner  in  which 
Nfitiire,  the  great  iirchitect  and  de^'oriitor,  uses  her 
material,  distrihiites  iiiid  strengthens  Iut  lines,  covers 
and   heautilies   surfaces,  would    reveal    tlie   laws  that 


l-on.Ms  ny  l.h.iVKs  AMI  H.nWh.HS. 


it;i( 


I  Nktur*. 

at  li  tlic  clc- 
tli(>    li'ut';    lit 

t    !*]llk|)tt  ({ivi'M 

•riiiii''-<      hill. 

|ii'titai^i)tial, 

'I'liki'    iMitirtt 

ciil    (irraiij^c- 

UIIll    StUIIII'IIH 
of  tilt'    HkW- 

ri'  tlic  Ifiil'  at 
at  il  ill  till' 
niitl  Hiin|il<', 
yiiiiMt'tricully 
H  riu'liij*. 
iiy  sliiiiiltl  hn 
I  (HTtaiii  <>x- 
ntli  (Irawiiijr 
111'  jH'iicil   of 

villl'M.   flTIIS, 

ill  iirawiii^', 
di/.c(l,  all  till) 

<|uii'k<'ii  till) 
iiiciT  art  of 
III',  and  tliu8 
I'll^jo  ill  till* 
ncr  ill  which 
tor,  usi's  lier 

lines,  I'oviTH 
U'   laws  that 


miiiithi'ol»'>M'il  ill  [iriu'tual  .h'sinii.  if  wi- woiiM  sn-iiri' 
th.'  ha|»|»it'Ht  I'fli'.'ts.  Thus,  in  n  irrfain  .h'^'r.-i'.  to 
iiiiiti'  hotiiiiy,  ilrawiiiK-  in»<l  ilt"<iK":"W'  wmhl  li'»t 
only  ph'iiHi'  iinil  profit  all,  cvi'H  yoiniK  iliihln-ii,  hut 
it  is  an  I'lisy  tiling  to  do  wlii'ii  tln-ri'  is  a  will    to  <lo 

it. 

Hi'liin  with  a  haf.  any  h'af,  th.-   pupils  h«'iii«  sup- 
plii'il  with  ni'wly-Kiithi'ri'il  oni's.     This  is  ainon^  llm 
lirst  .lucstions  to  h.-  asknl :  What  is  tlu)  j,'i'in'ral  form 
of  till'  h-af'.'     That    of  tlii-  liirli'.  .'llipsf,  oval,  trian- 
^U',  pi'iitiigon  'i    Then  would  follow  tho  minor  distim- 
tiouH  of  cordiforni,di  Itoid,  hiistati-,  etc     What  is  the 
character  of  thi'  margin  ■/     Is  it  ciitirf,  sirratc,  rt'- 
l.aiid.  lolu'd,  or  soiiu'thinK'  t'l""'-'     '^''^  'Vf"  *'«»  '''"• 
and  vi'iiis  distril>ut«!d,  and  do  thoy  miito  taii(,'«'ntially, 
or  othcrwisi'V     As   you  proceed,  thrro  will   ''c   such 
(piestioiis    as    these:    What    lessons    in    syniinetrical 
arrangement  ahoiit  a  centre,  aloiiK  an  axis,  are  to  hu 
learned   from  simple   leaves,   compound   haves,  from 
the  petals  and  stamens  of  flowers  V     What  lessons  in 
radiation  I'lom  a  parent  stem  arc   to  he   learned  Irom 
deeply-lohed  and  compound  leaves   and  from    tlower- 
nnihcls?     What  lessons    in   continuous  development 
foriovcring  irrcjjular  and  other  surfaces  can   vines, 
trailing,  climhing,  twiniiiK,  and  axillary  iiitlorcsceiice, 
teach  us?     What  lessons   in   hrcadth,  in    repose,  can 
we  learn  from  all?     Nature  lias  a  ivady  response  for 
each  of  these  i|Uestions,  whenever  we  choose  to  inter- 
rogate her  in   a  proper  manner.     lUit,  while   she   is 
answering   the  ipiestioiis  put  hy  the   student  of  art, 
she  can,  at    the    same    time,    answer    many    «>f    the 
(piestions  put  by  the  student  of  science. 


170 


TKAt'ltKHS'   ilASVAL 


Tiiu  i'X<<r  !iN«H  un  tl"*  nnxt  t>aK<*  art*  )(ivi>ti  for  tMWh* 
iTn  wlio  liikVH  a<-i|ulrtMl  noinu  mUiII  hi  tirnwin^;.  to  juit 
oil  iIk'  •miirtl  ni|>i<ily  Wlon'  tln'ir  rlnHmju.  'Ihcy  an' 
({ivi'ii  lii>n*  im-n-Iy  an  «uj(mmtiv<i  of  a  widf  viirnily  of 
«>x<>rciiioM  ulihili  tenulicrt*  iiiuy  urn*  to  inuki*  tlicir  drnw- 
iiig-leMf.!)!)!!  iiiturvMtiiig  to  thi-ir  |iii|iilM.  Tlic  <lniwiiif(N 
of  the  worm,  tho  i  liryNali!*,  uri<l  tli«  l)uttcrtii*>M,  un* 
■iiii|>I<>  illuMtnUioiiH  cf  how  tlic  <lruwing-(«XpreiH»if  iiiiiy 
bfl  iiMidu  tho  iii)*ana  of  t«n<'hing  niiioh  viihiitblc  knowl- 
edge, iw  w^ll  HH  (l))V<dopiiig  tho  luipiN'  p'rcfjitive 
fiicultioM.  Wliat  an  intoroMting  loHHon  in  nutiirul  hiit« 
tory  can  bo  nindo  from  theno  BimpK*  forini),  cvi'ii 
though  thoy  \m  hut  roughly  executed !  Th«  autlior 
of  tIliM  littio  work  looks  forward  confidently  to  tlie 
timo  when  drawing  in  [)uiilic  Hchoola  Hliall  not  ho  con- 
Ridcrcd  merely  aa  an  MXcrciHo  by  itstdf,  but  wIkmi 
teacherH  Mhall  line  their  xkill  in  drawing  largely  to 
illuMtrato  and  teach  many  other  branchvii  of  Htudy. 


Qi'KSTiONs.  -  What  li  Hiiid  of  tho  unc  of  geomotrical  fomm 
by  Naturu'?  Itupcnt  the  botaiiiciil  terms  given.  Whtit  i»  iniil 
alwut  i|ucitti<)niiiK  pupilit  in  their  drawiiit;  of  (lowom,  le«vc«,  &o.f 
What  U  laid  about  tho  teaching  of  botany  in  primary  Krhaol* '( 
Iliiw  can  the  drawin^-cxcrrimH  bo  made  intcrettini; ?  How  can 
M\\  in  drawing  he  ompluyvd  in  leaching  ? 


ni'TI.INK  rOHMS  f^iH   rWAVIIKNS. 


171 


iWillg,  to   |Mlt 

I.     'I'lu'y  an' 

(l«<  viirM'ly  of 

I!  tlipir  tlraw- 

Ihc  (IniwiiiffM 

ittfrtJicn,  iin' 

xpfciitei*  niuy 

iiublc  knowl- 

*    pTCfjitivw 

mitiirul  IiIm- 

rormM,  fvt  n 

Tli«  Rutlior 

ontly  to  tii« 

II  not  h«  con- 

If,  but  wlicn 

\^  hirgf'ly  to 

of  atuii^'. 


imotrical  fomm 
What  iit  mid 
on,  leavci,  &c.^ 
imnry  hcIiooIii  f 
nj;'    How  cnn 


A    H  VST  KM 

•I* 


Imlusirial  ami  Artistic  Dniwing 

KOn   PUBLIC   SCHOOLS. 

M.I.  IM,.U f    Wl  K.lu»l...n  ...   M««.h..«M.  *.-...Ml  S..,..r.l,..r  uf 

|>f<*inH  III  111.  Il>«t.m  rul''!'  *>'"■■">•.  *•"•  "I"'""  "'  '"• 


■Ihl,  ,yM.m  I-  ih,  unly  ...m,.«h«n,lvt  t.mr,.  .,|  In.irua.n..  u. 
a«*m«  .ccc.,lM.  •..  Ar,..rlcun  »cI..m,N.     Tl.r  cur,.  I,  ...  *f*>M  *- 

1.1  ihB  n.u-.t  ..Jv..n...l  0*.'  .1  »^  -  hluh  .cIuh.I. 
The  )<y»te.i>  •  nnnin^eH 
A  Primary  Cour««. 

An  Inter  Mediate  CourHe, 
A  /[irammar  CourHO, 

A  HlKh  School  Oourie. 

TIIK  I'KIMAKV  cmUNK. 

ThiH  c.mr.c  c...,iH.,  ..f  *  Munualfor  ll.«  u^c  „t  lf.ul.fr,,  i..  wlml, 
lli«  ,ln.pWclc...i-ni,  ..(  tl.f  .i...ly  »re  PHpta.ned  u.ul  in..,tr..UHl  1^  .!..• 
m.«t  f»mili..r  l.-..'  ..-.'I  .■^..-..l.l"i  ..ul  tw,.  scri.-,  ..(  C»r<K  cnu,,,. 

f  tlc«  o(  ...t  M»  -uil.  '4  C.nt.  ;   of  th.  Ci.dt,  IS  C«n1»  Mch. 
TIIK   lNTr.\MF,l)lATK  COURSE. 
Thl.  c....r«  ci.hWih  of  tVr»e  .mall  |)rawinK.|l.M.kH,  of  twenty  ,.aKC, 
fach.  sm  ..Al-y  ar'»n«.<l  f..r  (...piN  "Imm,  th.-v  l3e«i»  t"  dn.w  .m  p;.|M.r. 
The  exc.ci.fH  a.T  -f  ,.  .i..,.  4-  .l.,.r.u.rr  to  the  c.rel-cxo.nscs,  «ah  Ih- 
•ddltlolM.f  ,...'.. -I;..!.!*  ••  •"  i-^^  in  f.-i-h.wl  IVi^i.cctive. 
Thm  cui.r»e  .i1h»  n'nlivii    .i  -Mami.il  f"r  tiMchcrv 

r,K«  o'  Ih.  M.n^iil,  T4  Ctnti ;   of  th«  Book.  I!  Ctnt.  ..eh. 

'73 


J  >         +.» 


|i— w       ■  ■•* 


llli:    (.KAMMAK   COL'RSE. 


This  course  consists  i>(  :  — 
/•'inf.  I'"ouR  Hooks  in  1''kk|'.iianii  Outlink  Dkawinc  anh 
Dksicn.  The  exercises  in  tliesc  books  arc  more  advanced  tlian 
those  in  the  Intermediate  Course;  and  by  a  wide  variety  of  orna- 
mental, conventional,  and  natural  forms,  and  reprpsrntatioiis  of  his- 
torical ornau.ent,  pupils  are  taught  a  j;reat  deal  aljout  the  art  of  past 
..i|{cr.,  and  also  the  principles  of  guod  IJcsi^n. 

Sfifliii/.  FoiK  Hooks  in  (;i;omi;thi(  al  l)RA\viN(i.  These  l>ooks 
form  the  basis  for  I'erspective,  Model  and  Object,  and  Mechanical 
I>r:nvin«.  I  he  exercises  consist  of  problems  in  I'lane  (ieometry, 
the  uorkint;  of  which  teadies  pupils  the  exact  meaninf;  of  words  and 
terms:  and  by  the  rare  rc(|uired  to  execute  the  problems  they  are 
trained  to  accural  y  of  \vorkm.->nship. 

T/iik/.  Two  ItooKs  in  Mohel  and  Oii.ihi  t  Drawing;.  The 
exercises  in  tlicse  Ixioks  arc  all  in  outline;  and  pupils  arc  tauKht  in  a 
thorouKJi  manner  how  to  draw  from  objects.  The  exercises  are  of 
such  a  character,  that  tiie  pupil's  t.iste  will  be  cultivated  while  acfpiir- 
ing  skill  in  ilrawi:;;;. 

/•'oiirt/i.    Two   Hooks   in   I'kksit.ctivk   Di.awinc.      These  books 
teiich  the  elements  of  I'arallel  and  Anqubr  I'erspective. 
Kach  of  these  divisions  is  accompanied  by  a  M.inual  for  teachers, 

containilm  all  the  exercises  in  the  books,  ,ind  many  more  iK-sidcs. 

'Vice  of  the  Books.  S5  Cents  each. 

As  above  set  forth,  the  (irammar  Course  comprises  twelve  books; 
and  with  an  allowance  of  an  hour  and  a  half  to  two  hours  per  week 
to  drawiiiK.  pupils  can  easily  go  throuKli  three  of  these  books  in  a  year ; 
imd  when  pupils  have  linished  this  (irammar  Course,  they  will  be  able 
to  draw  in  outline  wluitever  they  can  see  and  understand. 

Where  pupils  in  ;;rainuuir  schools  have  received  no  previous  instruc- 
tion in  I'rcehanil  Drawiiii;.  the  f,rst  Kmdin-  of  the  instruction  must  be 
jiri  visional. 

Till'.  HK.ii  .SCHOOL  corusr.. 

This  c(  urse  consists  of  adv.nnced  work  in  I'e.  pectivp,  Mode!  and 
Object  DrawiuR,  or  Mechanical  Dr.iwins;,  according  to  the  t.astes  of 
pupils. 

As  in  the  previous  courses,  <inly  outline  work  has  been  .tttemptcd,  in 
ord?r  that  pupils  mijiht  become  well  grounded  in  all  the  elemcnt.-iry 
principles  of  Industriid  or  .Xrtistic  Dr-iwing,  when  they  reach  the  liigh 
'74 


1 


Ukawino  and 
re  aclvanccct  tlian 
le  variety  (jf  orna- 
'sriitatidiis  of  IiIn- 
(iiit  the  art  iil  past 

'iii.  These  Imoks 
t,  and  Mechanical 
I'lanc  (ieiinictry, 
linf;  of  words  aril 
)r<iblcins  they  are 

Drawint..  The 
ils  arc  taught  in  a 
:  exercises  are  of 
atcd  while  acqiiir- 

i;.  'I'hese  books 
tive. 

iiial  for  teachers, 
ore  besides. 


es  twelve  books ; 

)  hours  per  week 

e  lx)oks  in  a  year ; 

they  will  be  able 

ind. 

previous  instriic- 

struciion  must  be 


ctive,   Model  and 
to  the  tastes  of 

een  attempted,  in 
1  the  elementary 
ev  reach  the  liigh 


school,  they  will  bo  able  to  take  up  undcrstandintjly  the  more  advanced 
phases  of  the  study.  In  the  hifjli  school,  pr.pils  may  be  allowed  some 
election  in  their  course  of  study,  according  to  their  tastes  or  inclina- 
tions :  some  may  prefer  a  purely  artistic  course,  and  others  a  mechan- 
ical course.     Their  previous  training  lits  them  for  either  coi;rse. 

Hooks  for  this  course  are  in  preparation. 

The  lliRh  School  Course  includes  insiruction-in  Shading,  fainting, 
Drawing  from  Nature,  and  Desigmng  in  Color. 

This  System  is  a  I'RAtTicAULii  O.nh. 

It  is  frequently  represented  that  this  system  is  too  elalxirate  for 
public  sclu.ols.  It  may  be  said,  in  answer  to  this,  that  as  shading  an<l 
tigureilrawing,  &c.,  are  placed  at  the  end  of  the  course,  and  outline 
forms  are  used  to  give  the  elementary  instruction,  ample  time  is  secured, 
during  the  eight  to  twelve  years  of  school-life,  to  impart  a  sound 
knowledge  of  Drawing. 

This  system  proceeds  on  the  assumption  that  mere  hand-skill  in 
Driiwing  is  'f  secondary  importance;  that  Drawing,  like  writing, 
should  be  us'i'  i'rincipally  as  a  means  of  e.xpression. 

Starting  on  this  general  principle,  it  is  only  necessary  that  the 
knowledge  given  during  the  period  of  a  pupil's  school-life  should  Im: 
such  as  he  can  comprehend  in  the  course  of  his  advancement,  'i'he 
expression  of  this  knowledge  by  drawing  will  become  by  practice  of  no 
more  difficulty  than  expressing  thoughts  by  writing  ;  and  if  pupils  draw 
durini^  their  whole  school-course,  they  will  learn  to  draw  well  as  readily 
as  they  will  learn  to  read  or  write  well. 

This  Svstem  can  iik  xAoiiiiT  iiv  reoular  Tkai  hers. 

The  teachers'  manuals  which  accompany  the  bo<iks  give  full  particu- 
lars in  regard  to  teaching  each  subject ;  and  any  teacher,  with  a  little 
jiatient  study,  can  lit  himself  to  teach  iinderstandingly  and  well  what 
is  leouired  to  be  taught  below  the  High  School  Course. 

This  system  has  the  indorsement  of  some  of  the  leading  educators 
of  the:  country,  an'l  's  ra|)idly  being  introduced  into  public  schools. 
Although  the  books  have  been  published  but  a  few  months,  the  system 
has  been  adopted  by  the  Hoards  of  Education  of  the  following  cities  :  — 

Boston,  Lawrence,  Lowell,  Worcegter,  Oloiiccster,  Fltcli- 
biirK,  Tminton,  New  Beilfonl,  Newton,  Walthain,  Full  lUver, 
Uetlhani,  Woliurn,  ArllnKton.  Contord,  N.H.,  SnrntoRn 
Spr'nCK.  S.vrncuse,  PlttHbiirRh,  CoIunihiiH,  Detroit,  IndinnHp- 
olls,  Itlilwiiukee,  Onklnnil,  <'al.,  SBcrainento,  Cal.;  and  the 
I'rluiarj-  Course  Iiuh  been  adopted  for  the  Piibllt-  Schools'  of 
the  State  of  California. 

•75 


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